C. Pozrikidis: BISM Errata

Errata

Boundary Integral and Singularity Methods for Linearized Viscous Flow

C. Pozrikidis
Cambridge University Press, 1992

Page 9
Line 11: Should be: " If the flows u and u' are regular "
Page 11
Line 19: Change to: " ... particle of radius a are given by "
Line 23 up: Replace "the sphere" with "the particle"
Page 16
8 up: Change to; " ... it is often useful ..."
6 up: Should be: "u(t=0^-)=0, P(t=0^-)=0"
Page 19
2 up: At the end of this paragraph append the endnote superscript: "⁽¹⁾"
Page 22
Equation (2.2.23): The "I" on the right-hand side should be bold-faced: "I"
Page 28
4 up: Change to read: " ... a fluid executing rigid body motion ... "
Page 30
5 up: Replace "and character" with "or other special features"
Page 31
Line 2: Replace "Thus, we will reduce" with "In effect, we reduce"
Line 4: Replace "several solid boundaries" with "solid boundaries with several shapes"
Line 18: Add an endnote mark to read: "Figure 2.3.2(b)⁽²⁾."
Page 32
Line 9up: Replace "the body S_B" with "the body B"
Equation (2.3.27): At the lower side of the integral sign replace "S_B" with "B"
Page 33
Line 9: Replace "is a closed surface" with "is a closed surface D"
Line 8up: Cross out "the surface of"
Page 34
Line 3: Replace "on A" with "on S"
Line 9: Replace "potential," with "potential alone,"
Equation (2.3.33): In the second line the "+" sign should be a "-" sign.
Page 38
Line 7: Number this equation: (3)
Page 42
Line 7: Insert a comma after "Bakr" to read "Bakr,"
Page 43:
Line 3: Cross out the second minus sign on the right-hand side
Equation (2.4.18): Insert the argument "(l)" in between "bne^inf" to read: "bn(l)e^inf"
Equation (2.4.21): Row 2, Column 2: "I₁₀" should be "I₁₁"
Row 3, Column 3: "I₃₁" should be "I₁₁"
Page 44
Line 1: Insert endnote mark to read "...by one⁽³⁾, whereas"
Equation (2.4.23):    Row 2, Column 3 : "-1" should be: "-I₁₀"
                                 Row 3, Column 1: "(I₃₂-I₃₀)" should be "(I₃₀-I₃₂)"
                                 Row 3, Column 2: "1" should be "I₁₀"
Equation (2.4.24): Change the argument in the parenthesis on the LHS to read: (l₀, f₀)
Equation (2.4.24): Change the argument in the parenthesis on the RHS to read: (l₀)
Equation (2.4.25): The right-hand side should be: 8pmu_µn(l₀)
Line3 up: At the end of this section add the sentence: "Kim & Karrila (1991) discuss similar reductions of generalized double-layer representations discussed in Chapter 4 of this book."
Page 48
Line9 up: Change in three places to read: "...when the domain of integration Sp is replaced by an arbitrary surface that encloses Sp; in addition, for a force-free particle, they are independent of the choice of x_c (problem 2.5.1)."
Page 52
Line52: Change to read: "...the rotation of the particle ..."
Equation (2.5.34): Switch the two terms on the rhs to read: u_i(x) = w_k a³ ½e_klj((¶I_ij)/(¶x_0,1))(x, x₀)
Page 57
Line 17: Insert a comma to read "...to become a sphere, ..."
9 up: Replace "deduce" with "show"
Page 59
5 up: Enhance the end of this sentence to read "...sense discussed in section 2.3."
Page 60
Line 10: Replace "the delta function" with "the two-dimensional delta function"
Page 61
Equation (2.6.21): The "2" before the left parenthesis should be "4".
Equation (2.6.22): Hats should be placed on top of x and y.
Page 63
7 up: To the end of the paragraph add: "The origin is set at the centre of the circle."
6 up: Change "... flow D ..." to "... flow A ..."
5 up: Modify to read: "...to obtain for any function c"
2 up: Change "... into D." to "...into A."
Page 64
Line 16up: Change "potential dipoles" to "vortex dipoles"
Page 71
Line 9: Change "on the surface Sp" to "on the surface B"
Line 11: At the lower limit of the integral change "Sp" to "B"
Page 72
Equation (2.8.1): Change to: u_z(x₀) = ò_D [ - G^L(x, x₀)Ñu_z(x) + u_z(x) ÑG^L(x, x₀)]^. n dS(x)
Line 10: Insert a minus sign to read: Ñ²G^L=-5 up: Add an endnote mark to read: "(problem 4.1.3) ⁽⁴⁾."
Page 94
Equation (3.5.6): Please inert the superscript ``ST'' at the first two T on the right-hand side (thanks to Mark Blyth.)
Page 107
Line 6 up: Please change ``section 1.2'' to ``section 1.5''.
Page 108
15 up: Add an endnote mark to read: "for the density q.⁽⁵⁾"
Page 111
Line 12: Replace "which depend" with "that depend"
Page 115
Equations (4.5.4), (4.5.5): Replace after the "=" sign replace "q_j" with "q_i"
Page 125
Line 4: Should be: u^(k)=(I-a A") ^.u^(k)
4 up: Replace "behavior" with "behaviour"
Page 126
Line 5: Replace "requiring" with "stipulating"
11 up: Replace "unit normal vectors" with "unit vectors"
Page 128
Equation (4.7.2): The argument of the left-hand side should be bold-faced. Change "V_i(x₀)" to "V_i(x₀)"
Page 129
Equations (4.7.9), ( 4.7.10): Remove the argument "(x₀)" from the left-hand side.
Line 3: Replace "two-dimensional" with "three-dimensional"
Equation (4.7.11): Right after this equation add: "where X₀=x₀-x_c."
Page 132
Equation (4.8.11): Remove the superscript "-" from D at the lower side of the last integral.
Page 142
5 up: Modify to read: "(5.2.3), (5.2.8), and (5.2.9)..."
Page 147
Equation (5.5.1): Insert a pair of parentheses to read: Df = Dr (g ^.x) n + D { -P I + m[Ñu + (Ñu)^T]}^.n
Page 148
Equation (5.5.2): Enclose "g ^.x" with a pair of parentheses: "(g ^.x)"
Page 149
Line 10: Add an endnote mark to read: "whole space ⁽⁶⁾..."
Page 150
Line 11: Add some words to read: "...two curvilinear axes x and h that lie in the interface and measure arc length, and ..."
Page 151
Line 15: Modify to read: "... and x with the azimuthal arc length sf, ..."
Page 155
Equation (5.5.37) and at the next line: Change to bold to read: "e_s"
Page 157
Line 3: Strike out the word "ordinary"
Page 166
Line 17: Modify to read "...the first few derivatives of d|f|/db must be ..."
Page 174
Line 2: Change the denominators in the first two equations for f₁ and f₂ from a-1 to 1-a and from b-1 to 1-b.
Page 175
Line 3: Modify to read "... whose trace in the xy meridional ..."
Page 178
Line 4: Modify to read "where g=fh_n (see(6.2.12)). The coördinates of the base points and the corresponding weights w_n are indicated in Figure 6.4.1."
Page 180
Equation (6.4.10): The arguments of the integrand on the left-hand side should be (h, x, h₀, x₀,)
Page 194
Equation (7.2.16): The subscript "ijkl" at left-hand side should be "ijlk"
Page 203
12 up: Hat should be placed on top of x
2 up: Hat should be placed on top of x
Page 204
Line 3: The first sentence should be: "At this point we stipulate that Trace(q)=0."
Page 205
Line 14: Hat should be placed on top of x
7 up: Should be: (7.3.22) and (7.3.27)
Page 207
Line 18: Should read: (7.3.37) and (7.3.38)
Line 21: Should read: (7.3.35), (7.3.36), and (7.3.39)
Page 211
4 up: Should read: "and Kim & Karilla (1911, Chapter 13) present.."
Page 215
7 up: Change to read: " whereas when the fluid is stationary T=V/V."
Page 218
15 up: Delete " =0"
Page 224
Line 6: Change to read "condition u = W x (x-x_c)"
Page 225
Line 15: Change to read "... to a surface integral ..."
Page 228
4 up: Replace "where d is " with "and d is "
Page 229
Equation (11): Replace the whole equation with:
E=(i/4) H₀⁽¹⁾(-l²)^½(r)=(i/4)H₀⁽¹⁾(e^ip/4|l|r)=(1/2p)[ker₀(|l|r) - i kei₀(|l|r)]
Page 230
Equation (12) Strike out the first 9 lines up to the end of this problem and replace with:

All of these functions may be computed accurately using polynomial approximations (Abramowitz & Stegun 1972, p.384). Substituting (11) into (2) we find
                                                H= - 1/(2pl²) [ ln r + ker₀(|l|r) - (i kei₀(|l|r)]                                        (12)
Substituting further (12) into (2.2.4), and carrying out the differentations we find the Green's function
                                                G_ij(x, x₀) = d_ij A(R) + (^x_i^x_j)/r²   B (R) - i 2/|l|²   (d_ij/r²   -   2 (^x_i^x_j)/r⁴)
where R=|l|r, and the functions A and B are defined as follows
    A(x) = 2 [ ker₀ (x) - kei'₀(x) / x] - 2 i [ kei ₀(x) - ker'₀(x) / x]                                                                 (15)
    B(x) = 2 [ - ker₀ (x) + 2 kei'₀(x) / x] + 2 i [ kei₀(x) + 2 ker'₀ (x) / x]                                                     (16)
The pressure vector is given by (2.6.19).
Page 236
Problem 4.2.2: Replace "S_B" with "B" at two places in the text and in the equation.
Page 237
Problem 3: Change to read "...at a rate that is slower..."
1 up: Change in one place to read: [v ^.(A-l₂*I)²] ^.u = (l₁-l₂*) [v ^.(A-l₂*I)] ^.u = (l₁-l₂*)²v ^.u = 0
Page 244
Problem 6.4.2:
First equation: Change the subscript "i-1" to "i" in two places
Second equation: Change the subscript "i-1" to "i" in four places
Right after the first equation add: "where the point x₀ lies on the straight segment subtended by the points P_iand P_i+1."
Page 245
Line 11 up: Modify to read: "Using (7.2.2) and assuming the pressure vanishes at infinity, we find that ..."
Page 246
Equation 6: Add "a²" inside [] to read: [1 + l /(2*(5l+2)) a²Ñ²]₀
Line 4up: Should be: q = (1/6) a⁵ (l/(1+l)) E
Page 254
Second line of reference to Mikhlin
Please replace "Mechamics" by "Mechanics".