High order residual distribution for steady state problems for hyperbolic conservation laws}
For computational scientists solving hyperbolic conservation laws, this work offers a novel method that combines residual distribution with WENO for steady-state problems, but it is incremental as it adapts existing techniques.
The paper proposes a high-order residual distribution conservative finite difference scheme for steady state conservation laws, using a new WENO-ZQ integration to achieve high accuracy and shock resolution, as demonstrated by numerical examples.
In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state conservation laws. A new type of WENO (weighted essentially non-oscillatory) termed as WENO-ZQ integration is used to compute the numerical fluxes and source term based on the point values of the solution, and the principles of residual distribution schemes are adapted to obtain steady state solutions. Extensive numerical examples in both scalar and system test problems in one and two dimensions demonstrate the efficiency, high order accuracy and the capability of resolving shocks of the proposed methods.