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：Lax-Wendroff通量重构（LWFR）是一种用于求解双曲守恒律的单步、高阶、免求积方法。本文将LWFR格式推广至自适应网格加密（AMR）曲线网格上的守恒律求解。该格式采用基于子单元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。证明了所提出的LWFR格式向曲线网格的推广在标准度量恒等式下能保持常数解（自由流保持）。对于曲线网格，线性傅里叶稳定性分析无法用于获取最优CFL数。因此，提出了一种基于嵌入误差的LWFR方法时间步长计算方案，该方案减少了基于波速时间步长计算中为选择稳定CFL数所需的精细调参过程。所开发的方法通过可压缩欧拉方程进行验证，测试了混合限制器、可容许性保持、AMR算法、曲线网格及基于误差的时间步进方法。