This paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four general weights are determined by applying the Taylor series expansions. (2) These general weights are optimized to the new weights which are derived from the WENO concept and modified wavenumber approach. (3) No dissipation errors are found for the developed OCRWENO‐LD scheme through Fourier analysis. The proposed high‐resolution scheme demonstrates its capability in exhibiting high‐accuracy in smooth regions and avoiding numerical oscillation near discontinuities when simulating the wave equation, Burgers' equation, one‐dimensional Euler equation, porous medium equation, and convection–diffusion Buckley–Leverett equation.

中文翻译：

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对流问题的优化紧凑重构加权基本非振荡方案

本文提出了一种优化的紧凑型重建加权基本非振荡方案，该方案无耗散误差（OCRWENO-LD），用于解决对流问题。这种没有耗散误差的优化方案的构建过程如下：（1）我们首先设计一个高阶紧凑差分方案，该方案具有四个通用权重，连接四个低阶紧凑模板。通过应用泰勒级数展开式确定四个一般权重。（2）将这些一般权重优化为从WENO概念和改进的波数方法得出的新权重。（3）通过傅立叶分析发现，开发的OCRWENO-LD方案没有耗散误差。