标题： 隐式双重时间推进保持正性熵稳定格式用于可压缩纳维-斯托克斯方程 显示英文标题

标题： Implicit dual time-stepping positivity-preserving entropy-stable schemes for the compressible Navier-Stokes equations

摘要： 我们将在[30, 34]中开发的用于三维(3D)可压缩纳维-斯托克斯方程的显式高阶保正熵稳定谱配置格式推广到时间隐式公式。 时间导数项通过使用适合分别求解稳态和非稳态粘性流在高雷诺数下的第一和第二阶隐式后向差分公式(BDF1和BDF2)进行离散。 每个物理时间步的离散方程非线性系统通过使用双重时间步进技术进行求解。 所提出的方案具有可证明的熵稳定性和保正性，并在物理时间上提供无条件稳定性特性。 针对具有强激波和接触间断的超音速粘性流，给出了展示新双重时间步进方案准确性和保正性的数值结果。 显示英文摘要

摘要： We generalize the explicit high-order positivity-preserving entropy-stable spectral collocation schemes developed in [30, 34] for the three-dimensional (3D) compressible Navier Stokes equations to a time implicit formulation. The time derivative terms are discretized by using the first- and second-order implicit backward difference formulas (BDF1 and BDF2) that are well suited for solving steady-state and time-dependent viscous flows at high Reynolds numbers, respectively. The nonlinear system of discrete equations at each physical timestep is solved by using a dual time-stepping technique. The proposed scheme is provably entropy-stable and positivity-preserving and provides unconditional stability properties in the physical time. Numerical results demonstrating accuracy and positivity-preserving properties of the new dual time-stepping scheme are presented for supersonic viscous flows with strong shock waves and contact discontinuities.