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 -