In this paper, we present the development of a third-order density-based solver within the OpenFOAM framework, tailored for handling compressible flows. The solver incorporates implicit variational reconstruction on three-dimensional unstructured meshes, as well as a novel technology coupling reconstruction and time integration for both steady and unsteady simulations. To address the challenge of achieving high-order accuracy for curved geometries, we introduce a new approach for curved wall boundary reconstruction, specifically designed for situations where high-order mesh information is not readily available in OpenFOAM. Furthermore, we propose a simple WBAP limiter capable of capturing shocks without necessitating the whole-domain successive limiting procedure. Numerical tests were conducted to assess the solver's performance. The results reveal that our established solver exhibits higher accuracy in smooth flow simulations, while maintaining an excellent balance between accuracy and robustness for problems involving strong shocks and other complex flow structures.

在本文中，我们介绍了 OpenFOAM 框架内基于三阶密度的求解器的开发，该求解器专为处理可压缩流而定制。该求解器结合了三维非结构化网格上的隐式变分重建，以及用于稳定和非稳定模拟的耦合重建和时间积分的新技术。为了解决实现弯曲几何形状高阶精度的挑战，我们引入了一种用于弯曲壁边界重建的新方法，该方法专门针对 OpenFOAM 中不易获得高阶网格信息的情况而设计。此外，我们提出了一种简单的 WBAP 限制器，能够捕获冲击，而无需全域连续限制程序。进行数值测试来评估求解器的性能。