Application of a Discontinuous Petrov-Galerkin (DPG) method for simulation of compressible viscous flows in three dimensions is presented. The approach enables construction of stable schemes for problems with a small perturbation parameter. The main idea of the method is a weak formulation with a relaxed interelement continuity of the solution. The formulation satisfies the inf-sup condition with the stability constant independent of the small perturbation parameter, which here is the viscosity constant for the compressible Navier-Stokes equations. The DPG discrete formulation uses the specially designed so-called optimal test functions. They do not compromise the inf-sup stability of the continuous formulation. DPG does not use any artificial dissipation for the compressible Navier-Stokes equations. Being a residual minimization method it has got a built-in a posteriori error estimation which allows for mesh adaptivity leading to resolving reliable viscous fluxes, the major difficult task in simulations of viscous flows. We illustrate the method with a few steady state laminar solutions.

介绍了不连续 Petrov-Galerkin (DPG) 方法在三维可压缩粘性流模拟中的应用。该方法能够为具有小扰动参数的问题构建稳定的方案。该方法的主要思想是弱公式，具有松弛的解的元素间连续性。该公式满足 inf-sup 条件，其稳定性常数与小扰动参数无关，这里是可压缩 Navier-Stokes 方程的粘度常数。DPG 离散公式使用专门设计的所谓最佳测试函数。它们不会损害连续制剂的 inf-sup 稳定性。DPG 不对可压缩 Navier-Stokes 方程使用任何人工耗散。后验误差估计允许网格自适应，从而解决可靠的粘性通量，这是粘性流模拟中的主要困难任务。我们用一些稳态层流解决方案来说明该方法。