Asymptotic High-Order Schemes for Dissipative Hyperbolic Systems
D Aregba-Driollet, M Briani, R Natalini - SIAM Journal on Numerical Analysis, 2008 - SIAM
D Aregba-Driollet, M Briani, R Natalini
SIAM Journal on Numerical Analysis, 2008•SIAMWe investigate finite difference schemes which approximate 2*2 one-dimensional linear
dissipative hyperbolic systems. We show that it is possible to introduce some suitable
modifications in standard upwinding schemes, which keep into account the long-time
behavior of the solutions, to yield numerical approximations which are increasingly accurate
for large times when computing small perturbations of stable asymptotic states, respectively,
around stationary solutions and in the diffusion (Chapman–Enskog) limit.
dissipative hyperbolic systems. We show that it is possible to introduce some suitable
modifications in standard upwinding schemes, which keep into account the long-time
behavior of the solutions, to yield numerical approximations which are increasingly accurate
for large times when computing small perturbations of stable asymptotic states, respectively,
around stationary solutions and in the diffusion (Chapman–Enskog) limit.
We investigate finite difference schemes which approximate one-dimensional linear dissipative hyperbolic systems. We show that it is possible to introduce some suitable modifications in standard upwinding schemes, which keep into account the long-time behavior of the solutions, to yield numerical approximations which are increasingly accurate for large times when computing small perturbations of stable asymptotic states, respectively, around stationary solutions and in the diffusion (Chapman–Enskog) limit.
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