TY - JOUR

T1 - Finite-difference methods for one-dimensional hyperbolic conservation laws

AU - Berkenbosch, A.C.

AU - Kaasschieter, E.F.

AU - Thije Boonkkamp, ten, J.H.M.

PY - 1994

Y1 - 1994

N2 - This article contains a survey of some important finite-difference methods for one-dimensional hyperbolic conservation laws. Weak solutions of hyperbolic conservation laws are introduced and the concept of entropy stability is discussed. Furthermore, the Riemann problem for hyperbolic conservation laws is solved. An introduction to finite-difference methods is given for which important concepts such as, e.g., conservativity, stability, and consistency are introduced. Godunov-type methods are elaborated for general systems of hyperbolic conservation laws. Finally, flux limiter methods are developed for the scalar nonlinear conservation law.

AB - This article contains a survey of some important finite-difference methods for one-dimensional hyperbolic conservation laws. Weak solutions of hyperbolic conservation laws are introduced and the concept of entropy stability is discussed. Furthermore, the Riemann problem for hyperbolic conservation laws is solved. An introduction to finite-difference methods is given for which important concepts such as, e.g., conservativity, stability, and consistency are introduced. Godunov-type methods are elaborated for general systems of hyperbolic conservation laws. Finally, flux limiter methods are developed for the scalar nonlinear conservation law.

U2 - 10.1002/num.1690100207

DO - 10.1002/num.1690100207

M3 - Article

SN - 0749-159X

VL - 10

SP - 225

EP - 269

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -