A new numerical methodology to solve the 3D Navier-Stokes equations for incompressible fluids within complex boundaries and unstructured body-fitted tetrahedral mesh is presented and validated with three literature and one real-case tests. We apply a fractional time step procedure where a predictor and a corrector problem are sequentially solved. The predictor step is solved applying the MAST (Marching in Space and Time) procedure, which explicitly handles the non-linear terms in the momentum equations, allowing numerical stability for Courant number greater than one. Correction steps are solved by a Mixed Hybrid Finite Elements discretization that assumes positive distances among tetrahedrons circumcentres. In 3D problems, non-Delaunay meshes are provided by most of the mesh generators. To maintain good matrix properties for non-Delaunay meshes, a continuity equation is integrated over each tetrahedron, but the momentum equations are integrated over clusters of tetrahedrons, such that each external face shared by two clusters belongs to two tetrahedrons whose circumcentres have positive distance. A numerical procedure is proposed to compute the velocities inside clusters with more than one tetrahedron. Model preserves mass balance at the machine error and there is no need to compute pressure at each time iteration, but only at target simulation times.

提出了一种新的数值方法，用于求解复杂边界和非结构体拟合四面体网格内的不可压缩流体的3D Navier-Stokes方程，并通过三篇文献和一项真实案例测试进行了验证。我们应用分数时间步长程序，在该程序中依次解决了预测变量和校正变量问题。通过使用MAST（时空行进）过程解决了预测步骤，该过程明确处理了动量方程中的非线性项，从而允许Courant数大于1的数值稳定性。校正步骤通过混合混合有限元离散化解决，该离散化假定四面体周向中心之间的距离为正。在3D问题中，大多数网格生成器都提供了非Delunay网格。要为非Deelaunay网格保持良好的矩阵属性，一个连续性方程在每个四面体上积分，但动量方程在四个四面体簇上积分，这样，两个簇共享的每个外表面都属于两个四面体，它们的圆周中心具有正距离。提出了一种数值程序来计算具有一个以上四面体的团簇内部的速度。模型可在发生机器错误时保持质量平衡，并且无需在每次迭代时都计算压力，而仅在目标仿真时计算压力。提出了一种数值程序来计算具有一个以上四面体的团簇内部的速度。模型可在发生机器错误时保持质量平衡，并且无需在每次迭代时都计算压力，而仅在目标仿真时计算压力。提出了一种数值程序来计算具有一个以上四面体的团簇内部的速度。模型可在发生机器错误时保持质量平衡，并且无需在每次迭代时都计算压力，而仅在目标仿真时计算压力。