WENOCLAW: A higher order wave propagation method. (English) Zbl 1138.65084
Benzoni-Gavage, Sylvie (ed.) et al., Hyperbolic problems. Theory, numerics and applications. Proceedings of the 11th international conference on hyperbolic problems, Ecole Normale Supérieure, Lyon, France, July 17–21, 2006. Berlin: Springer (ISBN 978-3-540-75711-5/hbk). 609-616 (2008).
From the introduction: Many important physical phenomena are governed by hyperbolic systems of conservation laws
\[ {\mathbf q}_t+f({\mathbf q})_x = 0,\tag{1} \]
for which a wide range of numerical methods have been developed. In this paper we present a numerical method for solution of (1) that is also applicable to general hyperbolic systems of the form
\[ {\mathbf q}_t +A({\mathbf q},x,t){\mathbf q}_x =0.\tag{2} \]
In the nonlinear nonconservative case, the method may be applied if the structure of the Riemann solution is understood. Examples of (1–2) include acoustics and elasticity in heterogeneous media.
The method described in this work combines the notions of wave propagation and the method of lines, and can in principle be extended to arbitrarily high order accuracy by the use of high order accurate spatial reconstruction and a high order accurate ordinary differential equation solver. In this work, we use Runge-Kutta methods.
For the entire collection see [Zbl 1126.35003].
\[ {\mathbf q}_t+f({\mathbf q})_x = 0,\tag{1} \]
for which a wide range of numerical methods have been developed. In this paper we present a numerical method for solution of (1) that is also applicable to general hyperbolic systems of the form
\[ {\mathbf q}_t +A({\mathbf q},x,t){\mathbf q}_x =0.\tag{2} \]
In the nonlinear nonconservative case, the method may be applied if the structure of the Riemann solution is understood. Examples of (1–2) include acoustics and elasticity in heterogeneous media.
The method described in this work combines the notions of wave propagation and the method of lines, and can in principle be extended to arbitrarily high order accuracy by the use of high order accurate spatial reconstruction and a high order accurate ordinary differential equation solver. In this work, we use Runge-Kutta methods.
For the entire collection see [Zbl 1126.35003].
MSC:
| 65M20 | Method of lines for initial value and initial-boundary value problems involving PDEs |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 35L65 | Hyperbolic conservation laws |
