Numerical Approximation of Hyperbolic Systems Containing an Interface
This work provides a numerical solver for coupled hyperbolic systems with interfaces, relevant for applications like multiphysics models, but the method is incremental as it extends existing central schemes to a specific interface setting.
The paper presents a numerical method for approximating solutions of coupled hyperbolic conservation laws with a fixed interface, using a central scheme that balances wave effects at the interface. The method is well-balanced for piecewise constant equilibria and preserves conservation properties, with numerical tests demonstrating its quality across various applications.
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which interface conditions are linking the traces of both sides. The numerical solver is based on central methods, like the Rusanov scheme, and does not use the structure of the Riemann Problem. It consists in balancing the effects of the waves that enter the interface. The scheme is well balanced with respect to all the piecewise constant equilibria associated with the interface condition and is able to maintain exactly conservation properties of the interface conditions. A detailed analysis and several numerical tests show the quality of the method. Different applications, including sonic and transsonic flows and a multiphysic model are studied.