An implicit WENO scheme for steady-state computation of scalar hyperbolic equations

Weighted essentially non-oscillatory (WENO) schemes have proved useful in a variety of physical applications. They capture sharp gradients without smearing, and feature high order of accuracy along with nonlinear stability. The high order of accuracy, robustness, and smooth numerical fluxes of the WENO schemes make them ideal for use with Jacobian-based iterative solvers, to directly simulate the steady-state solution of conservation laws. In this paper, we consider a Newton-based implicit WENO solver for scalar conservation laws. A unique interpolation technique is developed, which produces a more efficient iteration. Numerical results are presented.