This directory contains a collection of Fortran and some C++ programs and subroutines on various aspects of numerical computation. This software accompanies the book: C. Pozrikidis, 1998, ``Numerical Computation in Science and Engineering,'' Oxford University Press. The level of difficulty varies over a broad range. Some programs are elementary and have been included for the purpose of familiarization with computer programming and numerical computation; other programs are more advanced.

The programs are arranged in twelve subdirectories. The first eleven directories correspond to the like-numbered chapters of the textbook. The twelfth directory contains programs for the evaluation of special functions. Stand-alone subroutines are accompanied by their drivers; if tintagel.f is the file name of a subroutine, then tintagel_dr.f is the name of the driver. Compilation and linking should be done as shown in the UNIX makefile of the host subdirectory, where the file dependencies are shown.

This directory is copied in identical form in the num_meth directory of the boundary-element library BEMLIB

Public subdirectories are printed in green.

Subdirectory	Subject
01_num_comp	General aspects of numerical computation
	Program Topic binary Converts a positive number to the corresponding binary. bits Greatest integer that can be described with a specified number of bits. cluster_2d Identifies clusters in a collection of point particles combinatorial Computes the combinatorial by two methods. euclid Finds the greatest common divisor of two positive integers. fast_sum Sums an infinite series whose terms decay like 1/n2. mapping Multiplies a vector by a matrix many times. pie Computes the number pi = 3.14... by considering the perimeter of a regular polygon with an increasing number of sides. prime Ascertains whether a specified integer is prime. ran_bsort Generates a string of random numbers and ranks them using bubble-sort. ran_sort Generates a string of random numbers, indexes them, and ranks them. richardson Accuracy improvement by repeated Richardson extrapolation. von_koch Generates the vertices of the von Koch periodic line.
02_lin_calc	Linear algebra and linear calculus
	Program Topic chol_c Cholesky decomposition of a symmetric and positive-definite matrix by column or row. det_33c Determinant of a 3x3 complex matrix det_44c Determinant of a 4x4 complex matrix det_hess Determinant of a lower or upper Hessenberg matrix. gram_sc Gram-Schmidt orhogonalization of a set of vectors. inv_l Inverse of a lower-triangular matrix. inv_u Inverse of an upper-triangular matrix. ldu LDU decomposition of a symmetric matrix. lu_c Crout LU decomposition, computation of the determinant and inverse of a matrix. lu_d Doolittle LU decomposition, computation of the determinant and inverse of a matrix. lu_d_t Doolittle LU decomposition of a tridiagonal matrix. qr_dec QR decomposition of an arbitrary matrix by three methods: Gram-Schmidt, rotation, and reflection.
03_lin_eq	Systems of linear algebraic equations
	Program Topic bcg Biconjugate gradients method for arbitrary systems. cg Conjugate gradients method for symmetric and positive-definite systems. cramer_22 Solution of a 2x2 system by Cramer's rule. cramer_33c Solution of a 3x3 complex system by Cramer's rule. cramer_44c Solution of a 4x4 complex system by Cramer's rule. cycl_red Cyclic reduction of a tridiagonal matrix with constant diagonal elements. gel Gauss elimination with option for partial pivoting and operation-reduction for a symmetric matrix; LU decomposition. gel_inv Computation of a matrix inverse by Gauss elimination. gel_mrhs Gauss elimination with multiple right-hand sides; computation of a matrix inverse. penta Solution of a pentadiagonal system. solve_chol_c Solution of a real, symmetric, and positive-definite system by Cholesky decomposition. thomas Solution of a tridiagonal system using Thomas's algorithm. thomas_c Solution of a tridiagonal system using a compact implementation of Thomas's algorithm. thomas_pr Solution of a tridiagonal system with two wrapped elements corresponding to periodic boundary conditions, using Thomas's algorithm.
04_nl_eq	Nonlinear algebraic equations
	Program Topic bairstow Bairstow's method for polynomial root finding. cubic Computes the roots of a cubic equation. fpi1 One-point iterations for one equation. fpi2 One-point iterations for two equations. non_lin Solves a system of nonlinear equations by the Newton or Broyden method. non_lin1 Solves one nonlinear equation by several methods. quadratic Computes the roots of the quadratic equation.
05_eigen	Eigenvalues and eigenvectors of matrices
	Program Topic char_poly Generates the coefficients of the characteristic polynomial by two methods. cond_number || ||2 condition number of a real matrix. house_sym Householder method for making a matrix tridiagonal. jacobi Jacobi method for computing all eigenvalues of a real symmetric matrix. lanczos Lanczos method for reducing a matrix to the tridiagonal form. lanczos_sym Lanczos method for reducing a symmetric matrix to the tridiagonal form. power Real eigenvalues of a real matrix by the power method with shifting and deflation and facility for inverse iteration. power_sym Real eigenvalues of a real symmetric matrix by the power method with shifting.
06_interp_diff	Function interpolation and differentiation
	Program Topic arc_3d Computes the circular arc that passes through three points in space. chebyshev Applications of Chebyshev interpolation and approximation. hermite Hermite interpolation of a function of one variable by two methods. interp_1d Interpolation of a function of one variable by several methods: Aitken, Fornberg, Neville, Newton lagrange Applications of Lagrange interpolation. lagrange_es Lagrange interpolation with evenly-spaced points. laplacian_2d Finite-difference formulae for the Laplacian of a function of two variables. splines_cb Cubic spline interpolation with several types of end-conditions.
07_integration	Numerical integration of a function of one or two variables
	Program Topic filon Filon rule for computing a sinusoidal integrand. gauss_disk Base points and weights for Gauss integration over a disk. gauss_lag Base points and weights of the Gauss-Laguerre quadrature. gauss_leg Base points and weights of the Gauss-Legendre quadrature for a regular integral. gauss_log Base points and weights of a quadrature for integrating an integrand with a log singularity. gauss_sph Base points and weights of a quadrature for integrating over the surface of a sphere. gauss_trgl Base points and weights of a quadrature for integrating over a planar triangle. integral Computes an integral of a function of one variable by several methods. integral_lag Computes an integral by the Gauss-Laguerre quadrature. integral_log Computes an integral with a logarithmic singularity using an appropriate quadrature.
08_approximation	Approximation of a function of one or two variables
	Program Topic b_spl_un Computes and displays uniform B-splines. b_splines Approximates a function with B-splines. bernstein Approximates a function with a Bernstein polynomial. fft Fast Fourier transform of a function of one variable. ft_1d Fourier transform of a function of one variable by the conventional method. ft_1d_nu Complex Fourier transform of a function of one variable with non-uniformly spaced points, computed by the conventional method. ft_2d Fourier transform of a function of two variables over a rectangle.
09_ode_ivp	Ordinary differential equations: initial-value problems
	Program Topic ode Solves a system of odes by several methods.
10_ode_bvp	Ordinary differential equations: boundary-value problems
	Program Topic fdm Finite-difference method for an ode. fem Finite-element method for an ode.
11_pde	Partial differential equations
	Program Topic chimney Temperature distribution in a chimney wall. poiss_DNDD Solution of Poisson's equations in a rectangle with Dirichlet and Neumann boundary conditions. poiss_NNNN1 Solution of Poisson's equations in a rectangle with Neumann boundary conditions. Equation is applied at interior and boundary nodes. poiss_NNNN2 Solution of Poisson's equations in a rectangle with Neumann boundary conditions. Equation is applied only at interior. rod Unsteady heat conduction through a rod.
12_spec_fnc	Computation of special functions
	Program Topic ber_bei_0 Computes the Kelvin functions ber0, bei0 and their derivatives. bess_I01K01 Computes the modified Bessel functions I0, I1, K0, K1 bess_J0 Computes the Bessel function J0. bess_J1 Computes the Bessel function J1. ell_int Computes the complete elliptic integrals of the first and second kind. error_f Computes the error function, the complementary error function, and the inverse error function. exp_int Computes the exponential integral. ker_kei_0 Computes the Kelvin functions ker0 and kei0, and their derivatives. gso_poly Generates the coefficients of several families of orthogonal polynomials using the Gram-Schmidt orthogonalization. leg_fnc_ortho Computes the orthonormal set of Legendre functions.

FDLIB main page and contents

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Directory: 02_grids

Grid generation in two and three dimensions

Public subdirectories are printed in green. The host BEMLIB directory is indicated when appropriate. The CFDLAB signature denotes that the graphics implementation of this program is available.

Subdirectory	Subject
grid_2d BEMLIB: grids CFDLAB	Discretization of a planar line into a collection of straight or circular elements with corresponding shapes.
prd_2d BEMLIB: grids	Adaptive parametrization of a closed line in the xy plane.
prd_2d_qs	Adaptive parametrization of a closed planar line with symmetry with respect to two planes.
prd_2d_pr	Adaptive parametrization of a periodic planar line.
prd_2d_pr_hs	Adaptive parametrization of a periodic planar line with symmetry with respect to the mid-plane.
prd_3d_cl	Adaptive parametrization of a closed three-dimensional line.
prd_3d_pr	Adaptive parametrization of a periodic three-dimensional line.
prd_ax BEMLIB: grids	Adaptive representation of a line beginning and ending at the x axis. The line is regarded as the trace of a surface of revolution in a meridional plane, generated by rotating the line around the x axis.
prd_ax_cl	Adaptive representation of a closed line. The line is regarded as the trace of a toroidal surface in a meridional plane.
prd_ax_hs	Adaptive representation of a line beginning and ending at the x axis, with plane-reflection symmetry with respect to the x=0 plane.
prd_ax_pr	Adaptive representation of a periodic line representing the trace of an axisymmetric periodic surface in a meridional plane.
prd_ax_pr_hs	Adaptive representation of a periodic line representing the trace of an axisymmetric periodic surface in a meridional plane, with plane-reflection symmetry with respect to the x=0 plane.
rec_2d CFDLAB	Interpolation and numerical differential of the velocity field through a two-dimensional rectangular grid, based on data provided at the grid nodes. Computation of the velocity gradient tensor, rate of deformation tensor and its eigenvalues and eigenvectors, vorticity and vorticity tensor.
rec_2d_strml CFDLAB	Interpolation and computation of streamlines and velocity vector field from data prescribed on a two-dimensional rectangular grid.
sm_3d_cl_tr	Smoothing of a function defined over a closed surface described by triangulation.
trgl BEMLIB: grids CFDLAB	Triangulation of a closed surface into an unstructured mesh of six-node curved triangular elements generated by the successive subdivisions of an octahedron or icosahedron.
trgl_octa_hs	Triangulation of an open surface into a structured grid consisting of six-node curved quadratic triangular elements. The triangulation descends from half the regular octahedron.
trgl_octa_sqr	Triangulation of a square patch into a structured grid of six-node plane triangular elements, based on the successive subdivisions of an eight-element pattern.

FDLIB main page and contents

FDLIB main page and contents

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Public subdirectories are printed in green. The host BEMLIB directory is indicated when appropriate. The CFDLAB signature denotes that the graphics implementation of this program is available.

Subdirectory	Topic
chan_2d	Couette-Poiseuille flow through a two-dimensional channel.
chan_2d_2l	Couette-Poiseuille flow of two superimposed layers through a two-dimensional channel.
chan_2d_imp CFDLAB	Transient flow flow in a channel confined between two parallel plane walls, due to the sudden translation of one wall parallel to itself with constant velocity.
chan_2d_ml CFDLAB	Flow of an arbitrary number of superimposed layers through a two-dimensional channel.
chan_2d_osc CFDLAB	Time-periodic Couette flow in a channel confined between two parallel plane walls, due to the in-plane oscillations of one of the walls.
chan_2d_trans CFDLAB	Transient flow in a channel confined between two parallel plane walls, due to the sudden application of a constant pressure gradient.
chan_2d_wom CFDLAB	Time-periodic flow in a channel confined between two parallel plane walls, due to an oscillatory pressure gradient.
chan_brush	Flow through a semi-infinite rectangular strip modeling the unit cell of a paint brush.
film	Flow of a film down an inclined plane.
films CFDLAB	Flow of an arbitrary number of superimposed layers down an inclined plane.
flow_1d CFDLAB BEMLIB: laplace	Steady, unidirectional, pressure- and gravity-driven flow through a tube with arbitrary cross-section. The main program solves an integral equation for the distribution of the boundary shear stress using a boundary-element method, and computes the velocity at a specified point.
flow_1d_1p BEMLIB: laplace	Steady, unidirectional, shear flow over a periodic array of cylinders or periodic wall with arbitrary cross-section. The main program solves an integral equation for the distribution of the boundary shear stress using a boundary-element method, and computes the drift velocity, the slip velocity, and the velocity at a specified point.
flow_1d_osc CFDLAB BEMLIB: helmholtz	Oscillatory, unidirectional, flow inside or outside a tube with arbitrary cross-section. The motion may be due to an oscillatory pressure gradient (internal flow), or to the translational oscillations of the tube wall parallel to the generators (internal or extrenal flow). The main program solves an integral equation for the distribution of the complex amplitude of the boundary shear stress using a boundary-element method, and then computes the complex amplitude of the velocity at a specified point.
plate_imp	Unsteady flow in a semi-infinite fluid bounded by an infinite plane, due to the impulsive translation of the plane at constant velocity.
plate_osc	Time-periodic flow in a semi-infinite fluid bounded by an infinite plane, due to the sinusoidal ocillations of theplane.
spf	Similarity solutions for three types of stagnation-point flow: Two-dimensional oblique stagnation-point flow toward a flat plate. Axisymmetric orthogonal stagnation-point flow toward a flat plate (Homman flow). Swirling flow due to the rotation of a flat disk (von Karman flow). The main program solves the boundary-value problem resulting from a similarity solution, using a shooting method.
strml	The main program generates streamline patterns for a braod range of flows listed in a nested menu, including, but not limited to, the following: Irrotational flows Periodic array of two-dimensional (2D) point sources. A 2D point source above a plane wall. A 2D point source in a channel. A 2D point source in a semi-infinite strip. A 2D oint source in front of a circular cylinder. A 2D potential dipole. A three-dimensional (3D) point source above a plane wall. A 3D point source in front of a sphere. A doubly-periodic array of 3D point sources. A 3D point source in uniform flow. Flow past a Rankine ovoid. A 3D potential dipole. A ring of point sources A ring of point sources near a wall. Flow around a corner. Flow past a stationary circular cylinder. Flow due to a moving circular cylinder. Flow past a flat plate. Flow past an ellipse. Flow past a Joukowski airfoil. Flow exiting a channel. Flow over a circular bump. Flow doen and up a strip. Flow past a sphere. Flow due to a moving sphere. Orthogonal stagnation-point flow past a sphere. Flow past a prolate spheroid. Flow past an oblate spheroid. Vortex flows Periodic array of Stuart vortices in shear flow. A pair of point vortices of equal strength. A point vortex outside a circular cylinder. A point vortex inside a circular cylinder. A point vortex between two walls. A point vortex in a semi-infinite strip. A periodic array of vortex blobs. A periodic vortex street. A line vortex ring. A line vortex ring in front of a plane. A line vortex ring in front of a sphere. A line vortex ring inside a sphere. Hill's spherical vortex in a stationary or moving frame. Stokes flows Stagnation-point flow against a plane wall. Flow due to a plane scraping a plane for several scraping angles. Flow due to a moving belt. Flow due to a tape plunging into a pool. Symmetric and antisymmetric flow in a corner. Flow due to the application of constant shear stress at a corner. Flow past, or due to, a translating sphere. Flow past, or due to, a translating drop. A three-dimensional points force (Stokeslet). A two-dimensional points force (Stokeslet). A doubly-periodic array of two-dimensional point forces. A triply-periodic array of three-dimensional point forces. A point force in front of a sphere. A point force above a plane wall. Linear flow past a drop. Quadratic stagnation-point flow. Flow past a slender cylinder. Shear flow over a plane wall with a circular orifice. Shear flow over a plane wall with a discoidal zero-shear-stress patch. Shear flow over a plane wall with a slit. Shear flow over a plane wall with a slit-like zero-shear-stress patch. Other flows Kovasznay flow. Taylor cellular flow. Oseen flow due to a moving sphere. Flow due to a point source of momentum. Blasius boundary-layer flow. Oblique stagnation-point flow toward a flat plate. Axisymmetric stagnation-point flow toward a flat plate. Two-dimensional linear flow.
tube_ann	Flow through an annular tube confined between two coaxial cylinders.
tube_ann_ml CFDLAB	Flow of an arbitrary number of annular layers through an annular tube confined between two coaxial cylinders.
tube_ann_sw	Swirling flow in an annular tube confined between two coaxial cylinders, due to the rotation of the inner or outer cylinder.
tube_ann_sw_ml CFDLAB	Swirling flow of an arbitrary number of annular layers in an annular tube confined between two coaxial cylinders, due to the rotation of the inner or outer cylinder.
tube_crc	Flow through a circular tube.
tube_crc_ml	Flow of an arbitrary number of annular layers through a circular tube.
tube_crc_sec	Flow through a circular tube due to the translation of section of the wall.
tube_crc_sw	Swirling flow in a circular tube due to the sudden rotation of the cylinder wall at constant angular velocity.
tube_crc_trans CFDLAB	Transient flow through a circular tube, due to the sudden application of a constant pressure gradient.
tube_crc_wom CFDLAB	Time-periodic flow through a circular tube, due to an oscillatory pressure gradient.
tube_ell	Flow through a tube with elliptical cross-section.
tube_rec	Flow through a tube with rectangular cross-section.
tube_trgl_eql	Flow through tube whose cross-section is an equilateral triangle.

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Directory: 05_lub

Lubrication flows

FDLIB main page and contents

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Directory: 06_stokes

Stokes flow

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Public subdirectories are printed in green. The host BEMLIB directory is indicated when appropriate. The CFDLAB signature denotes that the graphics implementation of this program is available.

Subdirectory	Subject
caps_2d	Dynamical simulation of the motion of a two-dimensional bubble, drop, or liquid capsule with generalized interfacial properties, in infinite, semi-infinite, or channel flow. The interface may exhibit constant surface tension, variable surface tension due to the presence of a surfactant, or develop elastic tensions due to the deformation from the unstressed shape. The evolution of the concentration of an insoluble surfactant over the deforming interface is computed by a semi-implicit finite-volume method. In the case of infinite flow, the program also computes the effective rheological properties of a dilute suspension.
caps_3d	Dynamical simulation of the motion of a three-dimensional bubble, drop, or liquid capsule bounded by an elastic membrane, in infinite or wall-bounded flow. The interface may exhibit constant surface tension, variable surface tension due to the presence of a surfactant, or develop elastic tensions and bending moments. due to the deformation from the unstressed shape. The evolution of the concentration of an insoluble surfactant over the deforming interface is computed by a semi-implicit finite-volume or finite-element method. In the case of flow in an infinite domain, the program also computes the effective rheological properties of a dilute emulsion.
caps_ax	Dynamical simulation of the deformation of an axisymmetric bubble, drop, or capsule, moving under the action of gravity, or deforming under the action of a specified infinite, semi-infinite, or tube flow. The interface may exhibit constant surface tension, variable surface tension due to the presence of a surfactant, or elastic tensions. The evolution of the concentration of an insoluble surfactant over the deforming interface is computed using a finite-volume method.
drop_3d	Dynamical simulation of the motion of a three-dimensional drop or bubble with uniform surface tension.
drop_3dw	Dynamical simulation of the deformation of a three-dimensional drop or bubble adhering to a plane wall with a specified contact line, under the influence of a shear flow. The interface exhibits constant surfce tension.
em_2d	Dynamical simulation of the motion of a singly- or doubly-periodic, polydisperse suspension of two-dimensional bubbles, drops, or capsules, subject to a specified shear flow. The interfaces may exhibit constant surface tension, variable surface tension due to the presence of a surfactant, or elastic tensions. The evolution of the concentration of an insoluble surfactant over the deforming interfaces is computed using a finite-volume method. The program also computes the effective rheological properties of the emulsion.
films	Dynamical simulation of the deformation of a number of superposed viscous layers comprising a composite film, for several flow configurations including: layers in channel flow, layers leveling on a horizontal plane, layers flowing down an inclined plane.
flow_2d BEMLIB: stokes CFDLAB	Flow in a two-dimensional domain with arbitrary geometry. The main program solves an integral equation of the first kind for the distribution of the boundary traction, and then computes streamlines emanating from specified points in the flow. Several types of flow and domain geometries are implemented in the program; other configurations can be included by straightforward additions.
flow_3x	Shear flow over an axisymmetric cavity, orifice, or protrusion embedded on a plane wall, possibly in the presence of an upper plane wall. The main program solves a system of integral equations of the first kind for the Fourier coefficients of the boundary distribution of the traction, and computes streamlines. In the case of flow over a protrusion, the program also computes the force and torque exerted on the protrusion. The program may be readily modified to handle shear flow past an axisymmetric particle, where the unperturbed flow is directed perpendicular to the particle axis.
layers	Dynamical simulation of the deformation of two superposed viscous layers, or one layer resting on a wall underneath a semi-infinite fluid, for a variety of configurations including: two layers in channel flow, a layer leveling underneath a semi-infinite fluid on a horizontal plane, a layer flowing down an inclined plane, an infinite interface deforming under the influence of a periodic collection of point-source dipoles.
prtcl_2d BEMLIB: stokes CFDLAB	Flow past a collection of two-dimensional particles with arbitrary shapes for several flow configurations including: Uniform flow past a doubly-periodic particle array, flow in a semi-infinite domain bounded by a plane wall, flow in a channel confined by two parallel plane walls. The main program solves an integral equation of the first kind for the distribution of the traction over the particle surfaces, and then generates streamlines emanating from specified points. The results allow the computation of macroscopic flow variables including the permeability of a disorderded two-dimensional porous medium. Flow past a fixed bed of two-dimensional particles with arbitrary shapes, for a variety of flow configurations, computed by a boundary-element method.
prtcl_2d_se	Same as prtcl_2d, except that the integral equations are solved using a spectral-element method.
prtcl_3d BEMLIB: stokes	Flow past, or due to the motion of, a three-dimensional solid particle in a solitary or periodic arrangememt. The main program solves an integral equation of the first kind for the distribution of the traction over the particle surface, and computes the grand-resistance tensor for rigid-body motion in a quiescent fluid. The flow occurs in an infinite domain or in a semi-infinite domain bounded by a plane wall. The force and torque exerted on a particle that is held stationary in an arbitrary flow may be computed readily from the numerical results using the reciprocal relation for Stokes flow. The translational and angular velocity of a particle subjected to a specified force and torque arises by a straightfoward computation.
prtcl_ax BEMLIB: stokes	Axisymmetric flow past, or due to the motion of, a collection of particles with arbitrary shapes aligned with a common axis, for a variety of configurations including: uniform flow past a fixed collection of particles, flow due to particle translation, flow in a semi-infinite domain bounded by a plane wall, flow in the interior of a cylindrical tube. The main program solves an integral equation of the first kind for the boundary traction, and then computes streamlines.
prtcl_sw BEMLIB: stokes	Swirling flow generated by the rotation of an axisymmetric particle around its axis. The main program solves an integral equation of the first kind for the distribution of the traction over the particle surface, and then computes the torque exerted on the particle. Several particle geometries are implemented in the program; others can be included with straightfoward additions.
sgf_2d BEMLIB: stokes	Green's functions of two-dimensional Stokes flow, representing the flow due to a two-dimensional point force. The subroutines evaluate the Green's functions for the velocity, pressure, and stress. Subroutine Topic sgf_2d_1p_fs Periodic Green's function in free space. sgf_2d_1p_w Periodic Green's function in a semi-infinite domain bounded by a plane wall. sgf_2d_1p_ww Periodic Green's function in a channel bounded by two parallel plane walls. sgf_2d_2p Doubly periodic Green's function. sgf_2d_2p_glut Generates look-up tables for the doubly periodic Green's function. sgf_2d_fs Free-space Green's function. sgf_2d_w Green's function in a semi-infinite domain bounded by a plane wall.
sgf_3d BEMLIB: stokes	Green's functions of three-dimensional Stokes flow, representing the flow due to a solitary point force or a periodic array of point forces. The subroutines evaluate the Green's functions for the velocity, pressure, and stress. Subroutine Topic sgf_3d_2p Doubly-periodic Green's function. sgf_3d_3p Triply-periodic Green's function. sgf_3d_fs Free-space Green's function. sgf_3d_sph Green's function for flow in the exterior of a solid sphere. sgf_3d_w Green's function for a semi-infinite domain of flow bounded by a plane wall.
sgf_ax BEMLIB: stokes	Green's functions of axisymmetric Stokes flow, representing the flow due to a ring of point forces. The subroutines evaluate the Green's functions for the velocity, and the kernel of the double-layer potential. Subroutine Topic sgf_ax_1p Singly-periodic Green's function in free space. sgf_ax_1p_ct Singly-periodic Green's function for flow inside a circular tube. sgf_ax_fs Free-space Green's function. sgf_ax_w Green's function for semi-infinite flow bounded by a plane wall.
susp_2d	Dynamical simulation of the motion of a collection of two-dimensional (cylindrical) particles with arbitrary shapes, for several flow configurations: uniform flow of a doubly-periodic array, flow in a semi-infinite domain bounded by a plane wall, flow in a channel bounded by two parallel plane walls. A specified force and torque is exerted on each particle. The main program solves an integral equation of the first kind for the distribution of the traction over the particle surfaces, and simultaneously produces the particle translational and angular velocities.
susp_2d_se	Same as susp_2d, except that the integral equations are solved using a spectral-element method.
thread_ax	Dynamical simulation of the evolution of an infinite liquid thread or annular layer, subject to axisymmetric periodic perturbations. The ambient fluid may be of infinite extent or bounded by a coaxial cylindrical surface in the configuration of the core-annular flow. The thread interface may exhibit constant surface tension, variable surface tension due to the presence of an insoluble surfactant, and develop elastic tensions. The evolution of the concentration of an insoluble surfactant over the deforming interface is computed by a finite-volume method.

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Directory: 07_ptf

Potential (irrotational) flow.

Public subdirectories are printed in green. The host BEMLIB directory is indicated when appropriate. The CFDLAB signature denotes that the graphics implementation of this program is available.

Subdirectory	Subject
airf_2d	Shapes of two-dimensional airfoils. Program Function joukowski joukowski airfoils by conformal mapping.
airf_2d_cdp	Potential flow past an airfoil with arbitrary geometry, with the Kutta condition satisfied at the trailing edge or at a designated point. The flow is computed by solving Laplace's equation subject to Dirichlet boundary conditions, using the constant-source-dipole panel method.
airf_2d_csdp	Potential flow past an airfoil with arbitrary geometry, with the Kutta condition satisfied at the trailing edge or at a designated point. The flow is computed by solving Laplace's equation with Dirichlet boundary conditions using the constant-point-source / source-dipole panel method.
airf_2d_lvp CFDLAB BEMLIB: laplace	Potential flow past an airfoil with arbitrary geometry, with the Kutta condition satisfied at the trailing edge or at a designated point. The flow is computed by solving Laplace's equation using the linear vortex panel method.
body_2d CFDLAB BEMLIB: laplace	Potential flow past a two-dimensional body with arbitrary geometry. The flow occurs in an infinite domain or in a semi-infinite domain bounded by a plane wall. The main program solves an integral of the second kind for the boundary distribution of a properly defined disturbance potential over the surface of the body, computes the distribution of the pressure coefficient and the force exerted on the body, and then computes streamlines originating from specified points. The program implements uniform flow past a body with cicrular, elliptical, triangular, or rectangular shape. Other flow geometries and types of flow may be included by straightforward modifications.
body_ax CFDLAB BEMLIB: laplace	Potential flow past an axisymmetric body with arbitrary geometry. The main program solves an integral equation of the second kind for the boundary distribution of a properly defined disturbance potential, computes the distribution of the pressure coefficient and the force exerted on the body, and then computes streamlines originating from specified points. The program implements uniform flow past a body with spherical, spheroidal, and toroidal shape. Other flow geometries and types of flow may be included by straightforward modification.
bubble_3d	Dynamical simulation of the evolution of a three-dimensional gas bubble suspended in an inviscid fluid. The ambient fluid is infinite or semi-infinite bounded by a plane wall. The flow is computed using a generalized vortex method with a boundary-element implementation.
cvt_2d CFDLAB	Potential flow in a rectangular cavity with impenetrable bottom and side walls, computed by a finite-difference method.
drop_3d	Dynamical simulation of the natural oscillations of a three-dimensional inviscid drop induced by surface tension. The flow is computed using a generalized vortex method with a boundary-element implementation.
flow_2d CFDLAB BEMLIB:laplace	Potential flow in a two-dimensional domain with arbitrary geometry. The main program solves an integral of the second kind for the boundary distribution of a properly defined disturbance harmonic potential, and then computes streamlines originating from specified points. The program implements uniform flow past a cavity or a protrusion embedded on a plane wall, possibly in the presence of an upper wall. Other flow geometries may be included by straightforward addition.
lgf_2d BEMLIB:laplace	Green and Neumann functions of Laplace's equation in two dimensions. These subroutines evaluate the following Green's functions and their gradient: Subroutine Function lgf_2d_1p Singly-periodic Green's function in free space. lgf_2d_fs Free-space Green's function. lgf_2d_w Green's function for a semi-infinite domain of flow bounded by a plane wall. lgf_2d_ww Green's function for flow in a channel confined between two parallel plane walls. lnf_2d_crc Neumann function for internal or external flow bounded by a circular cylinder. lnf_2d_w Neumann function for a semi-infinite domain of flow bounded by a plane wall. lnf_2d_ww Neumann function for flow on a channel confined between two parallel plane walls. lnf_2d_www Neumann function for flow in a semi-infinite rectangular strip confined between two parallel plane walls and another plane wall intersecting them at right angle.
lgf_3d BEMLIB:laplace	Green and Neumann functions of Laplace's equation in three dimensions. These subroutines evaluate the following Green's functions and their gradient: Subroutine Function lgf_3d_2p Doubly-periodic Green's function. lgf_3d_2p_glut Generates look-up tables for the doubly-periodic Green's function. lgf_3d_fs Free-space Green's function. lgf_3d_w Green's function for semi-infinite flow bounded by a plane wall. lnf_3d_sph Neumann function for flow inside or outside a sphere. lnf_3d_w Neumann function for flow in a semi-infinite domain bounded by a plane wall.
lgf_ax BEMLIB:laplace	Green's and Neumann functions of Laplace's equation in an axisymmetric doman. These subroutines evaluate the following Green's functions and their gradient: Subroutine Function lgf_ax_fs Free-space Green's function. lgf_ax_w Green's function for semi-infinite flow bounded by a plane wall. lnf_ax_w Neumann function for semi-infinite flow bounded by a plane wall.
tank_2d CFDLAB BEMLIB:laplace	Dynamical simulation of the sloshing of a liquid inside a rectangular tank undergoing accelerating motion, computed by a boundary-element method. Joanna Brown has prepared an amusing animation flick.
wave_3d	Dynamical simulation of doubly-periodic gravity/capillary waves computed by a generalized vortex method.

Partial documentation is provided in the User Guide.

Public subdirectories are printed in green.

Subdirectory	Subject
ann_2l	Capillary instability of the interface between two annular layers placed between two concentric cylinders, in the presence of an insoluble surfactant.
ann_2l0	Capillary instability of the interface between two annular layers placed between two concentric cylinders in the presence of an insoluble surfactant, under conditions of Stokes flow.
chan_2l0	Instability of two-layers flow in a channel confined between two parallel plane walls, under conditions of Stokes flow.
film	Instability of a liquid film flowing down an inlined plane, under conditions of Stokes flow.
film_s	Instability of a liquid film flowing down an inclined plane in the presence of an insoluble surfactant, under conditions of Stokes flow.
prony	prony: Decomposition of a time series into normal modes expressing exponentially growing or decaying sinusoidal waves. wave: Decomposition of linear spatial waves into exponentially evolving normal modes.
rt0	Rayleigh-Taylor instability of a horizontal interface between two semi-infinite fluids in Stokes flow.
rt0w	Rayleigh-Taylor instability of and a film resting on a plane wall underneath a semi-infinite fluid, under conditions of Stokes flow.
sf_inv	Normal-mode stability of an inviscid shear flow with a velocity profile specified in analytic or discrete form.
thread_inv	Capillary instability of an inviscid thread suspended in an infinite ambient inviscid fluid with negligible density.
thread0	Capillary instability of viscous thread immersed in an infinite ambient viscous fluid, under conditions of Stokes flow.
vl	Kelvin-Helmholtz instability of an inviscid vortex layer with constant vorticity.
vs	Kelvin-Helmholtz instability of a vortex sheet.

FDLIB main page and contents

FDLIB main page and contents

FDLIB main page and contents

FDLIB main page and contents

Partial documentation is provided in the User Guide.

Public subdirectories are printed in green. The host BEMLIB directory is indicated when appropriate.

Subdirectory	Subject
ldr_3d BEMLIB: laplace	Solution of Laplace's equation in the interior or exterior of a three-dimensional domain subject to the Dirichlet boundary condition, computed using the boundary-integral formulation.
ldr_3d_2p	Solution of Laplace's equation in the upper or lower half-space subject to the Dirichlet boundary condition on a doubly periodic surface, computed using the double-layer formulation.
ldr_3d_ext	Solution of Laplace's equation in the exterior of a three-dimensional region subject to the Dirichlet boundary condition, computed using the completed double-layer formulation.
ldr_3d_int	Solution of Laplace's equation in the interior of a three-dimensional region subject to the Dirichlet boundary condition, computed using the double-layer formulation.
lnm_3d BEMLIB: laplace	Solution of Laplace's equation in the interior or exterior of a three-dimensional domain subject to the Neumann (natural) boundary condition, computed using the boundary-integral formulation.

FDLIB main page and contents

FDLIB home and contents