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Three-dimensional elliptic grid generation with fully automatic boundary constraints

机译：具有全自动边界约束的三维椭圆网格生成

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A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart1US patent 7231329.~1 presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C~2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C~2 continuity destroys the grid clustering near the boundaries.
机译：本文提出了一种生成光滑均匀聚类的三维结构化椭圆网格的新方法，该方法通过扩展作者先前提出的二维对等项美国专利7231329.〜1来制定三维边界约束。这种全自动程序消除了在给定体积网格的六个边界表面上手动指定衰减参数的需要。此处已针对火星科学实验室（MSL）几何形状（如飞机外壳和机盖），充气式气动减速器（IAD）几何形状和3D解析定义的几何形状演示了该程序。由于自动边界约束允许衰减参数作为方程式椭圆网格系统解决方案的一部分发展，因此新程序还可以针对此类几何图形生成单块网格。这些衰减参数不再是常规方法中指定的常数，而是给定边界表面上的广义坐标变量的函数。由于这些衰减函数在给定的边界上变化，因此可以将任意任意简单连接的边界周围的正交网格自动聚类，而不必将边界和相应的内部或外部域分解为用于生成网格的各种块。新的边界约束不仅限于简单连接的区域，还可以在内部的多个连接和隔离的区域周围制定。所提出的方法优于诸如代数和双曲线技术的其他网格生成方法，因为此处获得的网格是C〜2连续的，而代数或双曲网格的简单椭圆平滑以强制C〜2连续性会破坏网格附近的网格聚类。边界。

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