LeVeque, Randall J. Numerical methods for conservation laws. 2nd ed. (English) Zbl 0847.65053 Basel: Birkhäuser. x, 214 p. (1992). See the review of the first edition (1990; Zbl 0723.65067). Cited in 688 Documents MSC: 65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems 65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis 65H10 Numerical computation of solutions to systems of equations 35L67 Shocks and singularities for hyperbolic equations 35L65 Hyperbolic conservation laws 76W05 Magnetohydrodynamics and electrohydrodynamics 86A10 Meteorology and atmospheric physics 85A30 Hydrodynamic and hydromagnetic problems in astronomy and astrophysics 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76T99 Multiphase and multicomponent flows 76S05 Flows in porous media; filtration; seepage 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 35Q15 Riemann-Hilbert problems in context of PDEs 35Q35 PDEs in connection with fluid mechanics 76L05 Shock waves and blast waves in fluid mechanics Keywords:research exposition; shocks; weak solutions; Rankine-Hugoniot; entropy; characteristics; sound speed; nonlinear; Euler equations; isotropic flow; rarefaction waves; contact discontinuities; local error; Lax equivalence theorem; upwind methods; numerical dispersion; numerical dissipation; conservation form; approximate Riemann solver; modified conservation laws; sonic entropy fix; total variation stability; TVD; monotonicity; preserving; monotone methods Citations:Zbl 0723.65067 PDFBibTeX XMLCite \textit{R. J. LeVeque}, Numerical methods for conservation laws. 2nd ed. Basel: Birkhäuser (1992; Zbl 0847.65053)