Based on the analysis of the entropy condition scheme formulation, the accuracy order comes from initial value interpolation and flux reconstruction. Following the limiters of the traditional second-order Total Variation Diminishing scheme, higher accuracy order and non-oscillatory nature are retained with a newly proposed smoothness threshold method. Then, the scheme using the solution formula method in Dong et al. [(2002). High-order discontinuities decomposition entropy condition schemes for Euler equations. CFD Journal, 10(4), 563–568] is generalized to fully-discrete fourth-order accuracy, which retains the advantages of former schemes, i.e. it is a fully-discrete, one-step scheme with no need to perform with a Runge–Kutta process in time; an entropy condition is satisfied with no need of an entropy fix with artificial numerical viscosity; and an exact solution is achieved for linear cases if CFL→1. Numerical experiments are given with a 1D scalar equation for a shock-tube problem, a blast-wave problem, and Shu–Osher problem, a 2D Riemann problem, a double Mach reflection problem and a transonic airfoil flow problem for NACA0012. All tests are compared with a fifth-order Weighted Essentially Non-Oscillatory (WENO) scheme. Numerical experiments and efficiency comparisons show that the efficiency of the new fourth-order scheme is superior to the fifth-order WENO scheme.

基于对熵条件方案公式的分析，准确度顺序来自初始值插值和通量重构。遵循传统二阶总变差递减方案的限制器，新提出的平滑阈值方法保留了更高的精度阶数和非振荡性质。然后，使用Dong等人的求解公式方法的方案。[（2002）。欧拉方程的高阶不连续性分解熵条件方案。差价合约期刊, 10(4), 563–568] 被推广到完全离散的四阶精度，它保留了以前方案的优点，即它是一个完全离散的、一步的方案，不需要用 Runge–库塔过程及时；熵条件满足，不需要人工数值粘性的熵固定；如果 CFL→1，则对于线性情况可实现精确解。针对 NACA0012 的激波管问题、冲击波问题和 Shu-Osher 问题、二维黎曼问题、双马赫反射问题和跨音速翼型流动问题，给出了数值实验的一维标量方程。所有测试都与五阶加权基本非振荡 (WENO) 方案进行比较。