This paper extends a new class of positivity-preserving, entropy stable spectral collocation schemes developed for the one-dimensional compressible Navier-Stokes equations in [1,2] to three spatial dimensions. The new high-order schemes are provably L2 stable, design-order accurate for smooth solutions, and guarantee the pointwise positivity of thermodynamic variables for 3-D compressible viscous flows. Similar to the 1-D counterpart, the proposed schemes for the 3-D Navier-Stokes equations are constructed by using a flux-limiting technique that combines a positivity-violating entropy stable method of arbitrary order of accuracy and a novel first-order positivity-preserving entropy stable finite volume-type scheme discretized on the same Legendre-Gauss-Lobatto grid points used for constructing the high-order discrete operators. The positivity preservation and excellent discontinuity-capturing properties are achieved by adding an artificial dissipation in the form of the low- and high-order Brenner-Navier-Stokes diffusion operators. To our knowledge, this is the first family of positivity-preserving, entropy stable schemes of arbitrary order of accuracy for the 3-D compressible Navier-Stokes equations.

翻译：本文扩展了在[1,2]至三个空间维度为一维压缩纳维-斯托克方程式开发的新的一流的保正、稳固的光谱共位方案。新的高阶方案可以想象L2稳定,设计顺序准确,可以顺利解决问题,保证3D压缩透视流热动力变量的点性能。与1D对口类似,3-D导航-斯托克方程式的拟议方案是通过使用一个通量限制技术构建的,该技术结合了任意测准的假设-防扰-稳定方程式和新颖的一阶保正态-稳定的保正量组合,与用于建造高压离心操作器的同一Tultre-Gaus-Lobatto方位网点分开。与1D对口类似,3-Navier-Stoks等方程式的拟议保正性和极不连续性特性通过在这种低和高调Brenner-Navilate-Stopy-Strocro 稳定方程式中添加了一种人为分裂的精确度方法,这是我们家庭稳定方程式的保正对等方程式的系统。