classic papers in numerical simulation of conservation law

sunsky

R.Courant, E.Isaacson and M.Rees, On the solution of nonlinear hyperbolic differential equations by differences, Comm. Pure Appl. Math., 5 243(1952).
P.D.Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation, Comm. Pure Appl. Math., 7, 159(1954).
O.Oleinik, Discontinuous solutions of nonlinear differential equations, Amer. Meth. Soc. Transl. Ser.2, 26, 95(1957).
S.K.Godunov, A finite method for the computation of discontinuous solutions of the equations of fluid dynamics, Mat. Sb., 47, 357(1959).

P.D.Lax and B.Wendroff, Systems of conservation laws, Comm. Pure Appl. Math., 13, 217(1960).
C.E.Leith, Numerical simulation of the earth's atmosphere, in Methods in Computational Physics, Vol.4}丂(ed.by B.Alder et.al.), pp.1-28 (Academic Press, New York 1965
R.W.MacCormak, The effects of viscosity in hypervelocity impact cratering, AIAA Paper 69-354(1969).

J.P. Boris and D.L.Book, Flux corrected transport I, SHASTA, a fluid transport algorithm that works, J. Comp. Phys., 11, 38(1973).
D.K. Purnell, Solution of the advective equation by upstream interpolation with a cubic spline. Mon. Wea. Rev. , 104}, 42 (1975).
A.J.Chorin, Random choice solution of hyperbolic systems, J. Comp. Phys., 22, 517(1976).
R.F.Warming and R.W.Beam, Upwind second order difference schemes with applications in aerodynamic flows, AIAA Journal, 24, 1241(1976).
B. van Leer, Toward the ultimate conservative difference scheme. Part IV: A new approach to numerical convection. J. Comput. Phys., 23, 276(1977).
B. van Leer, Toward the ultimate conservative difference scheme. Part V: A second order sequel to Godunov's method. J. Comput. Phys., 32, 101(1979).
B.P.Leonard, A stable and accurate convective modeling procedure based on quadratic upwind interpolation, Comp. Method in Appl. Mech. and Eng., 19, 59 (1979)
S.T.Zalesak, Fully multidimensional flux corrected transport algorithm for fluids J. Comp. Phys., 31, 335(1979).
P.L.Roe, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comp. Phys., 43, 357(1981).
A.Harten, High resolution schemes for hyperbolic conservation laws, J. Comp. Phys. 49, 357(1983).
S.Osher, Rieman solvers, the entropy condition, and difference approximations, SIAM J.Num. Anal., 21, 995(1984).
T.Kawamura and K.Kuwahara, Computations of high Reynolds number flow around a circular cylinfer with surface roughness, AIAA paper 84-0340 (1984)
P.Colella and P.R.Woodward, The piecewise parabolic method (PPM) for gas-dynamical simulations, J. Comp. Phys., 54, 174(1984).
H.Takewaki, A.Nishiguchi and T.Yabe, Cubic interpolated pseudo-particle method (CIP) for solving hyperbolic-type equations, J. Comp. Phys., 61, 261(1985).
P.L.Roe, Characteristic-based schemes for the Euler equations, Annu. Rev. Fluid Mech. 18, 337(1986).
A. Harten and S. Osher, Uniformly hight-order accurate non-oscillatory schemes. I. SIAM J. Numer. Anal., 24, 279(1987).
A.Harten, ENO schemes with subcell resolution, J. Comp. Phys. 83, 148(1987).
A.Harten, B.Engquist, a.Osher and S.Chakravarthy, Uniformly high order accurate essentially nonoscillatory schemes, III, J. Comp. Phys. 71, 231(1987).
G.Moretti, Computation of flows with strong shocks, Annu. Rev. Fluid Mech., 19,313(1987).
H.C.Yee, A class of high-resolution explicit and implicit shock-capturing methods, Von Karman Institute for Fluid Dynamics, Lecture Series 1989-04(1989).
X.D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes., J. Comput. Phys. 115, 200(1994).
G.S. Jiang and C.W. Shu, Efficient implementation of ENO schemes., J. Comput. Phys., 126, 202(1996).

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