We extend the fourth order, two stage Multi-Derivative Runge Kutta (MDRK) scheme to the Flux Reconstruction (FR) framework by writing both stages in terms of a time averaged flux and then using the approximate Lax-Wendroff procedure to compute the time averaged flux. Numerical flux is carefully constructed to enhance Fourier CFL stability and accuracy. A subcell based blending limiter is developed for the MDRK scheme which ensures that the limited scheme is provably admissibility preserving. Along with being admissibility preserving, the blending scheme is constructed to minimize dissipation errors by using Gauss-Legendre solution points and performing MUSCL-Hancock reconstruction on subcells. The accuracy enhancement of the blending scheme is numerically verified on compressible Euler's equations, with test cases involving shocks and small-scale structures.

翻译：本文将四阶两阶段多导数龙格-库塔（MDRK）格式扩展至通量重构（FR）框架，其方法是将两个阶段均表示为时间平均通量的形式，并采用近似Lax-Wendroff格式计算该时间平均通量。数值通量的构造经过精心设计，以增强傅里叶CFL稳定性与计算精度。针对MDRK格式开发了基于子单元的混合限制器，该限制器可严格证明受限格式具有可容许性保持特性。在保持可容许性的同时，混合方案通过采用高斯-勒让德解点并在子单元上执行MUSCL-Hancock重构，以最小化耗散误差。通过对包含激波与小尺度结构的可压缩欧拉方程测试算例进行数值验证，证实了混合格式在精度提升方面的有效性。