A Finite Difference Mapped WENO Scheme with Unequal-Size Stencils for Hyperbolic Conservation Laws.

In this paper, a fifth-order finite difference mapped weighted essentially non-oscillatory scheme with unequal-size stencils, termed as MUS-WENO, is designed for hyperbolic conservation laws. The new mapping function and nonlinear weights are proposed to reduce the difference between the linear weights and nonlinear weights. It could get smaller numerical errors and obtain fifth-order accuracy, give optimal fifth-order convergence with a tiny ε even near critical points in smooth regions, and simultaneously suppress spurious oscillations near strong discontinuities. Comparing with the classical fifth-order finite difference WENO schemes and fifth-order finite difference mapped WENO (MWENO) schemes, this mapped WENO scheme uses three unequal-size stencils and the linear weights which can be any positive numbers on condition that their summation is one. Another advantage is that we can reconstruct polynomial over the whole big stencil, while many classical high-order WENO reconstructions only reconstruct the values at the boundary points or discrete quadrature points. Extensive examples including some steady-state problems and some low density, low pressure, or low energy extreme problems are used to testify the good representations of this new MUS-WENO scheme. [ABSTRACT FROM AUTHOR]