Premium
General hyperbolic difference formulas for linear and quasilinear hyperbolic equations
Author(s) -
Cushman John H.,
Huang ChiHua
Publication year - 1982
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650020406
Subject(s) - mathematics , hyperbolic partial differential equation , inviscid flow , mathematical analysis , dirichlet boundary condition , boundary value problem , boundary (topology) , linear equation , dirichlet distribution , partial differential equation , physics , mechanics
The method of non‐standard finite elements was used to develop multilevel difference schemes for linear and quasilinear hyperbolic equations with Dirichlet boundary conditions. A closed form equation of k th‐order accuracy in space and time ( O (Δ t k , Δ x k )) was developed for one‐dimensional systems of linear hyperbolic equations with Dirichlet boundary conditions. This same equation is also applied to quasilinear systems. For the quasilinear systems a simple iteration technique was used to maintain the k th‐order accuracy. Numerical results are presented for the linear and non‐linear inviscid Burger's equation and a system of shallow water equations with Dirichlet boundary conditions.