Symmetry-preserving enforcement of low-dissipation method based on boundary variation diminishing principle

A class of high-order shock-capturing schemes, PnTm-BVD (Deng et al., 2019; Deng 2020) have been devised to solve the Euler equations with substantially reduced numerical dissipation, which enable high-resolution simulations resolve flow structures wider range scales. In such low errors round-off level might grow and contaminate solutions. typical example problems is loss symmetry in solutions for physical symmetric configurations even if schemes are mathematically line rules. this study, mechanisms symmetry-breaking a finite volume framework P4T2-BVD reconstruction scheme thoroughly examined. Particular attention has paid remove possible causes due lack associativity floating-point arithmetic associated errors. Modifications new techniques proposed completely breaking different components solver. Benchmark tests that solution used verify methods. The results demonstrate perfect structures.