We address here the discretization of the momentum convection operator for fluid flow simulations on 2D triangular and quadrangular meshes and 3D polyhedral meshes containing hexahedra, tetrahedra, prisms and pyramids. The finite volume scheme that we use for the full Euler equations is based on a staggered discretization: the density unknowns are associated with a primal mesh, whereas the velocity unknowns are associated with a "fictive" dual mesh. Accordingly, the convection operator of the mass balance equation is derived on the primal mesh, while the the convection operator of the momentum balance equation is discretized on the dual mesh. To avoid any hazardous interpolation of the unknowns on a possibly ill-defined dual mesh, the mass fluxes of the momentum convection operator are computed from the mass fluxes of the mass balance equation, so as to ensure the stability of the resulting operator. A coherent reconstruction of these dual fluxes is possible, based only on the kind of considered polygonal or polyhedral cell, and not on each cell itself. Moreover, we show that this process still yields a consistent convection operator in the Lax-Wendroff sense, that is, if a sequence of piecewise constant functions is supposed to converge to a a given limit, then the weak form of the corresponding discrete convection operator converges to the weak form of the continuous operator applied to this limit. The derived discrete convection operator applies to both constant and variable density flows and may thus be implemented in a scheme for incompressible or compressible flows. Numerical tests are performed for the Euler equations on several types of mesh, including hybrid meshes, and show the excellent performance of the method.
翻译:我们在这里处理2D三角和方形间距和3D多角度间距内含六赫德拉、四赫德拉、棱镜和金字塔的流流模拟动力对流操作器离散问题。 用于整个 Euler 方程式的有限体积图是根据一个交错的离散法设计的: 密度未知值与质平衡方程式的质量通量有关, 而速度未知值则与“ 幻觉” 双网格有关。 因此, 质量平衡方程的对流操作器的对流操作器在初线和三角间距和3D多面间距的对流中产生分流, 而势头平衡方形的对流的对流则分解。 为了避免在可能定义不清的双向双向的双向间距上出现任何未知的对流。 因此, 动力对流的大规模通量是根据质量平衡方格的通量计算, 以确保由此产生的操作器的稳定性。 这些双向通量的重组是可能的, 仅仅基于考虑的多角或对流的对流, 而对于每个运行的对流的对流的对流的对流的对流的对流的对流的对流, 我们的对流的对流的对流的对流的对流的对流的对流的对流的对流的对流的对流的对流, 将显示的对流的对流的对流的对流的对流的对流的对流进行, 显示显示的对流的对流的对流的对流的对流的对流的对流的对流的对流的对流是, 的对流的对流的对流的对流的对流的对流的对的对运行的对流的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对的对流进行,,对的对流是,对的对的对的对的对的对的对的对的对结果的对结果的对结果的对的对的对的对的对的对的对的对的对的对流是,,对流是,对的对的对的对的对的对的对