A Fixed-Point Fast Sweeping WENO Method with Inverse Lax-Wendroff Boundary Treatment for Steady State of Hyperbolic Conservation Laws

Abstract Fixed-point fast sweeping WENO methods are a class of efficient high-order numerical to solve steady-state solutions hyperbolic partial differential equations (PDEs). The Gauss-Seidel iterations and alternating strategy used cover characteristics PDEs in each order achieve convergence rate solutions. A nice property fixed-point which distinguishes them from other is that they explicit do not require inverse operation nonlinear local systems. Hence, easy be applied general system. To deal with the difficulties associated boundary treatment when finite difference on Cartesian mesh complex domains, Lax-Wendroff (ILW) procedures were developed as very effective approach literature. In this paper, we combine fifth-order method an ILW procedure solution conservation laws computing regions. Numerical experiments performed test solving various problems including cases physical aligned grids. results show accuracy good performance method. Furthermore, compared popular third-order total variation diminishing Runge-Kutta (TVD-RK3) time-marching for computations. examples most examples, saves more than half CPU time costs TVD-RK3 converge