A simple WENO-AO method for solving hyperbolic conservation laws

摘要

In this paper, we propose a simple weighted essentially non-oscillatory method with adaptive order(SWENO-AO). The SWENO-AO consists of a high order and a second-order subreconstructions with a new weight, in which the second-order subreconstruction is always smooth. Comparing to WENO-AO method developed by Zhu and Qiu (2016), the SWENO-AO has the advantage of simplicity. First, the SWENO-AO does not need to regroup the candidate cells, but uses the weighted-least-squares to obtain a smooth second-order subreconstruction directly, which is more flexible for solving multi-dimensional problem. However the WENO-AO needs to regroup the candidate cells properly for obtaining different second-order subreconstructions, so that near discontinuity, at least one of them is smooth and can be used for avoiding the spurious oscillations. Second, the SWENO-AO only consists of two subreconstructions, so the implementation is simple. However the WENO-AO uses more subreconstructions for higher dimensional problem, which increases the computational complexity. Finally, the weight of SWENO-AO is simpler than the one of WENO-AO. Numerical tests also show that, the SWENO-AO gives comparable solution as WENO-AO, but uses less computational cost, thus has higher efficiency.