Finite Volume Methods for Hyperbolic Problems
by
Line numbers include figure captions and section headings.
Negative line numbers indicate a number of lines up from the bottom of the page.
p. 18, last line: "q(x,t) =" should be "q(x,t_0) = "
p. 21, equation (2.24): there should not be a minus sign on the right.
p. 22, line -13 (displayed equation with integrals): First integral on right hand side should have a minus sign.
p. 33, line above (2.77): "\tilde A_{qx}" should be "\tilde Aq_x"
p. 46, Exercise 2.4: (2.51) should be (2.50).
p. 46, line -7: "where a is a constant", the first "a" should be italicized.
p. 50, line -12: "S(x) = 1 if -0.3 < x < -0.1" should be "S(x) = 0.5 if -0.3 < x < -0.1"
p. 55, first line of (3.28): "x < 0" should be "x \leq 0".
p. 58, the last vector in (3.35) should be r^3 rather than r^1.
p. 66, equation (4.8): the last term should not be divided by \Delta x.
p. 78, first displayed equation: the integrand should be f(q(x_{i-1/2},t)).
p. 83, line before (4.56): "Using (4.47) in (4.49)..." should be "Using (4.48) in (4.49)..."
p. 89, line -10: "claw/1d/example1" should be "claw/clawpack/1d/example1"
p. 91, line 11: unix> setenv MATLABPATH ".:\$CLAW/matlab"
should be unix> setenv MATLABPATH ".:$CLAW/matlab"
p. 94, line -8: "mx < maxmx" should be "mx \leq maxmx"
p. 99, line 9: Change last sentence to "See claw/applications/acoustics/1d/varying/interface for an example of the use of auxiliary arrays."
p. 103, line below (6.9): "defined in Section 4.12" should be "defined in (4.45) and (4.60)".
p. 107, equation (6.17): change leading minus sign in second line to plus.
p. 122, equation (6.66): change "k" in numerator of fraction to "\Delta t"
p. 124, line 4: "nonuniform gird" should be "nonuniform grid".
p. 127, line before (6.77): should read "but with the 1 replaced by \kappa_{i-1}/\kappa_{i-1/2}:"
p. 128, In Exercise 6.7, the expression for D_i^n, the subscripts i-1/2 and i+1/2 should be switched. (The first \theta should be \theta_{i+1/2} and both the numerator and denominator of the ratio should contain \theta_{i-1/2}.)
p. 131, Two lines below equation (7.4) Q_n^{n+1} should be Q_N^{n+1} .
p. 136 second eq. down from (7.14), W_1^1 should be W_1^2.
p. 142, line -13: "O(\Delta x^s) as s \goto 0" should be "... as \Delta x \goto 0".
p. 157, Problem 8.3(b) should read "provided $0 \leq \bar u \Delta t / \Delta x \leq 1$", since for the upwind version given in (a) we must assume $0 \leq \bar u \leq 1$.
p. 173, line after (9.51): B(x) = \Lambda(x) R_x^{-1}(x)R(x)
p. 177, two lines before (9.54): Section 2.8 should be 3.8.
p. 181, (9.66): Subscripts are reversed on the fluctuations.
p. 199, between (10.27) and (10.28): "to give give second-order accuracy" has an extra "give".
p. 215, equation (11.33): integral on right hand side should go from - infinity to infinity, rather than 0 to infinity.
p. 226, Exercise 11.7, the first line of the function definition should say x<0.
p. 228, line -10: "x/t=x_{i-1/2} is simply q_s" should read "(x-x_{i-1/2})/t =0 is simply q_s".
p. 236, line 7,8: there should be no tildes on the last three W's and the last W should have subscript i+1/2, so it reads " by comparing W_{i-1/2} to W_{i-3/2} or W_{i+1/2} depending on the sign of s_{i-1/2}".
p. 242, line 10, in the double integral, "dx" should be "dx dt".
p. 246, equation (12.46): under "\inf_{w \in W}" should be "\inf_{q \in W}"
p. 260, 262, 280, 286: Figures 13.5, 13.7, 13.16, and 13.20 all show the Riemann solution at time t=1.
p. 261, The third sentence of the third paragraph should read
"If the pth wave is a shock, then
characteristics of family 1 through p-1 will cross from right to left,
characteristics of family p+1 through m will cross from left to right, ..."
p. 261, line -7: "This as discussed" should be "This is discussed".
p. 263, displayed equation: "u_m = \epsilon \sqrt{g h_0}" should be "u_m = \epsilon \sqrt{g/h_0}"
p. 267, line -13: The value of h_m should be h_m = 1.5514.
(The value h_m = 2.1701 is for h_l=h_r=1, u_l=1, and u_r = -1.)
p. 282, line after (13.59): "then the solution consists of the these two shocks", Delete the second "the".
p. 284, equation (13.63): The second component of f(q) in the last form given should read (q^2)^2/q^1 + ....
p. 285, equation (13.64): The (2,1) entry in the first matrix should be -(q^2)^2/(q^1)^2 + g q^1.
p. 290, Exercise 13.12(c): "Lax Entropy Condition 11.1" should be 13.1.
p. 307, 308: Figures 14.3 and 14.4 both show the Riemann solution at time t=1.
p. 324, equation (15.46): There is a hat missing on "u_m" in the first line, it should read: "\lambda_m^1 = \hat u_m - ...".
p. 324, equation (15.47): The "-2(...)" in the second line should be "+2(...)" Line before equation (15.47): "using (13.33)" should be "using (13.32)"
p. 328, equation (15.60):
Top line: "\lambda_i^p" should be "\lambda_{i-1}^p"
Bottom line: "\lambda_{i+1}^p" should be "\lambda_i^p"
p. 328, line -8 and p. 329, line -14: "van Lear" should be "van Leer"
p. 332-333, captions to Figures 15.5 and 15.6: t = 0.38 should be t = 0.038.
p. 333, Figure 15.6:
The HLLE Riemann solver used to compute the results shown in Figure 15.6
had a bug.
The correct results look only slightly better.
See book/chap15/wcblast for the
corrected code and new figures.
p. 391, equation (17.43): The factor "\Delta t / 2" in the first line of this formula should be "\Delta t / 4".
p. 403, equation (17.82): "psi(w(x-st)/\tau)" should be " psi(w((x-st)/\tau))" on the left hand side.
p. 428, line after (18.32): The impedance is "Z_0 = \rho_0 c_0"
p. 443, equation (19.22): The integral should be divided by "\Delta x \Delta y".
p. 444, equation (19.28): "\Delta x" should be "\Delta y"
p. 445, equation (19.29): "\Delta x" in the second line should be "\Delta y"
p. 445, equation (19.29): "Q_{ij}^n" in the third line should be "Q_{ij}^{**}"
p. 454, Figure 20.4: the downward going waves should be labelled "v_{i-1,j-1/2}^- ..." rather than "v_{i-1,j+1/2}^- ..."
p. 470, equation (21.2): "(A^- + B^+)(A^- + B^+)" should be "(A^- + A^+)(B^- + B^+)".
p. 478, equation (21.26): The impedance "Z_{i,j+1}" in the numerator should be "Z_{ij}".
p. 481, equation (21.36): The last term in the numerator of the first line, "(h_r u_r - h_l u_l)" should be "(h_r v_r - h_l v_l)"
p. 481, equation (21.36): If u_r does not equal u_l then the expression (21.36) can be simplified to obtain (21.34) using the definition of u_hat. Hence use of the Roe average (21.34) does give a matrix $\hat A$ that satisfies the usual requirement (21.35) and the discussion at the bottom of this page should be deleted.
p. 496, equation (22.16): The entries "\mu" in the 4th and 6th rows of the matrix A should be "-\mu" (negated).
p. 510, equation (22.67): u = c_{pl} should be u = -c_{pl}.
p. 531, line -17, a left paren "(" is missing before "xlower". It should read "(xc,yc) = (xlower + ...".