We propose an efficient, accurate and robust IMEX solver for the compressible Navier-Stokes equation with general equation of state. The method, which is based on an $h-$adaptive Discontinuos Galerkin spatial discretization and on an Additive Runge Kutta IMEX method for time discretization, is tailored for low Mach number applications and allows to simulate low Mach regimes at a significantly reduced computational cost, while maintaining full second order accuracy also for higher Mach number regimes. The method has been implemented in the framework of the deal.II numerical library, whose adaptive mesh refinement capabilities are employed to enhance efficiency. Refinement indicators appropriate for real gas phenomena have been introduced. A number of numerical experiments on classical benchmarks for compressible flows and their extension to real gases demonstrate the properties of the proposed method.
翻译:我们建议为压缩的纳维-斯托克斯方程式提供一个高效、准确和强大的IMEX溶解器,配以一般状态方程式。该方法基于美元-美元适应性离散空间分解法和用于时间分解的Additive Runge Kutta IMEX方法。该方法针对低马赫数应用,允许模拟低马赫制度,计算成本大大降低,同时为较高马赫数制度也保持完全的第二级精确度。该方法已在交易框架内实施。二. 数字图书馆,其适应性网格改进能力被用于提高效率。引入了适用于实际气现象的精细指标。关于可压缩流动的经典基准及其对实际气体的延伸的一些数字实验显示了拟议方法的特性。