We extend the fourth order, two stage Multi-Derivative Runge Kutta (MDRK) scheme of Li and Du to the Flux Reconstruction (FR) framework by writing both of the stages in terms of a time averaged flux and then use the approximate Lax-Wendroff procedure. Numerical flux is computed in each stage using D2 dissipation and EA flux, enhancing Fourier CFL stability and accuracy respectively. 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Li和Du提出的四阶、双阶段双导数龙格-库塔(MDRK)格式推广至通量重构(FR)框架中，通过将两个阶段均用时均通量表示，并采用近似Lax-Wendroff方法。每个阶段使用D2耗散和EA通量计算数值通量，分别提升傅里叶CFL稳定性和精度。针对MDRK格式，本文开发了一种基于子单元的混合限制器，确保限制后的格式可证明保持容许性。该混合格式不仅保持容许性，还通过使用高斯-勒让德解点并在子单元上进行MUSCL-Hancock重构，将耗散误差降至最低。通过对可压缩欧拉方程进行数值验证，包括涉及激波和小尺度结构的测试案例，证实了混合格式的精度提升效果。