An Adaptive High Order WENO Solver for Conservation Laws (Communications in Computational Physics, 2019)
This paper presents an implementation of the adaptive hybrid WENO(weighted essentially non-oscillatory) scheme based on our previous investigationsfor compressible multi-medium flows (Liu and Hu, J. Comput. Phys., 342 (2017),43-65). In this study a simple and efficient method is developed for Euler equationsand Navier-Stokes equations arising from the conservation laws. A class of high order weighted essentially non-oscillatory (WENO) schemes are applied to resolve thecomplicated flow structures and shock waves. Classical WENO schemes are computationally expensive in calculating the non-linear weight and smoothness indicators. Wepropose a block-structured adaptive mesh method together with a modified hybrid-WENO scheme to reduce the cost, the reconstruction is only performed at non-smoothregion. Comparisons of WENO scheme with various smoothness indicators and different Lax-Friedrich flux vector splitting methods are performed on block structuredadaptive mesh. Benchmark tests show present adaptive hybrid WENO method is low-dissipative and highly robust. The 2-D/3-D shock wave boundary layer interaction aresimulated to verify the efficiency of present AMR (adaptive mesh refinement) solverin predicting turbulent flow
Keywords: Block-structured AMR; WENO; Euler equations; Navier-Stokes equations; large scale computation.