Lax-Wendroff Flux Reconstruction (LWFR) is a single-stage, high order, quadrature free method for solving hyperbolic conservation laws. This work extends the LWFR scheme to solve conservation laws on curvilinear meshes with adaptive mesh refinement (AMR). The scheme uses a subcell based blending limiter to perform shock capturing and exploits the same subcell structure to obtain admissibility preservation on curvilinear meshes. It is proven that the proposed extension of LWFR scheme to curvilinear grids preserves constant solution (free stream preservation) under the standard metric identities. For curvilinear meshes, linear Fourier stability analysis cannot be used to obtain an optimal CFL number. Thus, an embedded-error based time step computation method is proposed for LWFR method which reduces fine-tuning process required to select a stable CFL number using the wave speed based time step computation. The developments are tested on compressible Euler's equations, validating the blending limiter, admissibility preservation, AMR algorithm, curvilinear meshes and error based time stepping.

翻译：摘要：Lax-Wendroff通量重构（LWFR）是一种用于求解双曲守恒律的单步、高阶、无求积方法。本文将LWFR格式扩展至带有自适应网格细化（AMR）的曲线网格上求解守恒律问题。该格式采用基于子单元的混合限制器实现激波捕捉，并利用相同的子单元结构在曲线网格上获得可容许性保持。理论证明，所提出的LWFR格式在标准度量恒等式下可保持曲线网格上的常数解（自由流保持）。由于曲线网格无法采用线性傅里叶稳定性分析获得最优CFL数，本文针对LWFR方法提出了一种基于嵌入式误差的时间步长计算方法，减少了基于波速时间步长计算中为选择稳定CFL数所需的精细调试过程。通过可压缩欧拉方程组的数值试验，验证了混合限制器、可容许性保持、AMR算法、曲线网格及基于误差步进方法的有效性。