Hybrid Grid Generation for Viscous Flow Simulations in Complex Geometries

In this paper, we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions. Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent. With respect to marching direction, three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness. A novel weighted strategy is used in the normal smoothing scheme, which evidently reduce the possibility of early stop of front generation at complex corners. With respect to marching distances, the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first; a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries. These efforts, plus other special treatments such as multi-normal generation and fast detection of local/global intersection, as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

ABOUT SMOOTH INTERPOLATION OF A TRIANGULATED SURFACE

A method and algorithm for rebuilding a surface triangulation in three-dimensional space defined by an STL file is proposed. An initial surface in 3D space (STL file) is represented as a polyhedron composed of triangular faces. The method is based on the analytical representation of the surface as a piecewise polynomial function. This function is built on a polyhedral surface composed of triangles and satisfies the following requirements: 1) within one face, the function is an algebraic polynomial of the third degree; 2) the function is continuous on the entire surface and preserves the continuity of the first partial derivatives; 3) the surface determined by the function passes through the vertices of the initial triangulated surface. The restructuring of computational meshes is required in cases of distortion of the shape of cells when solving problems of mathematical physics using mesh methods (finite-difference, FEM, etc.). Cell distortion can be due to various reasons. These can be large distortions of moving Lagrangian meshes in the calculations in the current configuration, with instability of the hourglass type, with distortion of the faces of the interface between interacting gaseous, liquid and elastoplastic bodies. The rebuilding of the mesh reduces to solving the problem of constructing a smooth surface passing through the nodes of an existing triangulated surface or part of it. Later the nodes of the new mesh are placed on the constructed smooth surface with existing requirements for the size and shape of the cells. The construction of a smooth piecewise polynomial surface is based on the ideas of spline approximation and reduces to the building of a cubic polynomial on each triangular face, taking into account the smooth conjugation of polynomial pieces of the surface constructed on adjacent faces. The proposed method for rebuilding surface triangulation can be useful for calculating the motion of deformable bodies when solving problems of the dynamics of continuous media on immovable Euler grids.

STOCHASTIC SURFACE MESH RECONSTRUCTION

A generic and practical methodology is presented for 3D surface mesh reconstruction from the terrestrial laser scanner (TLS) derived point clouds. It has two main steps. The first step deals with developing an anisotropic point error model, which is capable of computing the theoretical precisions of 3D coordinates of each individual point in the point cloud. The magnitude and direction of the errors are represented in the form of error ellipsoids. The following second step is focused on the stochastic surface mesh reconstruction. It exploits the previously determined error ellipsoids by computing a point-wise quality measure, which takes into account the semi-diagonal axis length of the error ellipsoid. The points only with the least errors are used in the surface triangulation. The remaining ones are automatically discarded.