System and method of generating mesh representing flow domain
A system and method generates a mesh representing a flow domain around a surface of a physical object. The system receives an initial mesh representing the flow domain. The initial mesh has a corner vertex corresponding to a corner grid point of a grid in a parameterized space. The system updates the corner grid point to obtain an updated grid in the parameterized space according to angles formed by boundary edges and a border edge of the initial mesh. The system determines an updated mesh from the initial mesh according to the updated grid to reduce a difference between the angles formed by the boundary edges and the border edge. The system generates the mesh representing the flow domain for simulating a physical characteristic of the physical object.
1 . A computer-implemented method, comprising:
receiving, by a memory of a system, an initial mesh representing a flow domain around a surface of a physical object, wherein the initial mesh has a block mesh for a corner of the surface, wherein the block mesh includes a corner vertex, two boundary vertices, and a border vertex along outer edges of the block mesh, wherein boundary edges of the outer edges connect the two boundary vertices to the corner vertex for boundaries of the flow domain around the corner of the surface, wherein a border edge connects the corner vertex to the border vertex, wherein the initial mesh corresponds to a grid in a parameterized space according to a mapping relationship, and wherein the corner vertex of the initial mesh corresponds to a corner grid point of the grid;
updating, by one or more processors of the system, the corner grid point to obtain an updated grid in the parameterized space according to angles formed by the boundary edges and the border edge, the updated grid being obtained by maintaining fixed in the parameterized space other grid points corresponding to vertices along the outer edges of the block mesh;
determining, by the one or more processors, an updated mesh from the initial mesh according to the updated grid and the mapping relationship to reduce a difference between the angles formed by the boundary edges and the border edge; and
generating, by the one or more processors, a final mesh representing the flow domain for simulating a physical characteristic of the physical object.
2 . The computer-implemented method of claim 1 , wherein the initial mesh includes block-structured embedded meshes within a topology of the flow domain, wherein the topology includes a plurality of topology faces meeting at the corner of the surface, and wherein the border edge is a topology edge extending from the corner vertex between the plurality of topology faces.
3 . The computer-implemented method of claim 1 , wherein the grid includes a block grid corresponding to the block mesh, wherein the block grid has border grid points corresponding to the vertices of the outer edges of the block mesh, wherein the block grid has interior grid points corresponding to interior vertices of the block mesh, and wherein the interior grid points are linearly interpolated between the border grid points.
4 . The computer-implemented method of claim 1 , wherein updating the corner grid point includes moving the corner grid point in the grid without moving the corner vertex in the updated mesh.
5 . The computer-implemented method of claim 1 , wherein determining the updated mesh equalizes the angles formed by the boundary edges and the border edge.
6 . The computer-implemented method of claim 1 , wherein the mesh includes a plurality of secondary block meshes connected with the block mesh in a chain between the corner vertex for the corner of the surface and a boundary vertex for a boundary of a second surface of the physical object, wherein the chain corresponds to a chain grid of the grid, wherein the chain grid includes the corner grid point, an end grid point corresponding to the boundary vertex, and a plurality of chain grid points linearly interpolated between the corner grid point and the end grid point.
7 . The computer-implemented method of claim 1 , wherein the initial mesh has a plurality of face vertices along boundary edges of the surface between a first surface location and a second surface location, wherein the updated mesh includes face edges extending from respective face vertices, and wherein angles of the face edges relative to the boundary edges are based on a proximity of the respective face vertices to the first surface location or the second surface location.
8 . The computer-implemented method of claim 1 , wherein the updated mesh includes a mesh vertex connecting mesh edges having edge arclengths based on a number and a type of the mesh edges.
9 . A non-transitory computer-readable medium storing instructions executable by one or more processors of a system to cause the system to perform a method, comprising:
receiving, by a memory of the system, an initial mesh representing a flow domain around a surface of a physical object, wherein the initial mesh has a block mesh for a corner of the surface, wherein the block mesh includes a corner vertex, two boundary vertices, and a border vertex along outer edges of the block mesh, wherein boundary edges of the outer edges connect the two boundary vertices to the corner vertex for boundaries of the flow domain around the corner of the surface, wherein a border edge connects the corner vertex to the border vertex, wherein the initial mesh corresponds to a grid in a parameterized space according to a mapping relationship, and wherein the corner vertex of the initial mesh corresponds to a corner grid point of the grid;
updating, by one or more processors of the system, the corner grid point to obtain an updated grid in the parameterized space according to angles formed by the boundary edges and the border edge, the updated grid being obtained by maintaining fixed in the parameterized space other grid points corresponding to vertices along the outer edges of the block mesh;
determining, by the one or more processors, an updated mesh from the initial mesh according to the updated grid and the mapping relationship to reduce a difference between the angles formed by the boundary edges and the border edge; and
generating, by the one or more processors, a final mesh representing the flow domain for simulating a physical characteristic of the physical object.
10 . The non-transitory computer-readable medium of claim 9 , wherein the initial mesh includes block-structured embedded meshes within a topology of the flow domain, wherein the topology includes a plurality of topology faces meeting at the corner of the surface, and wherein the border edge is a topology edge extending from the corner vertex between the plurality of topology faces.
11 . The non-transitory computer-readable medium of claim 9 , wherein the grid includes a block grid corresponding to the block mesh, wherein the block grid has border grid points corresponding to the vertices of the outer edges of the block mesh, wherein the block grid has interior grid points corresponding to interior vertices of the block mesh, and wherein the interior grid points are linearly interpolated between the border grid points.
12 . The non-transitory computer-readable medium of claim 9 , wherein updating the corner grid point includes moving the corner grid point in the grid without moving the corner vertex in the updated mesh.
13 . The non-transitory computer-readable medium of claim 9 , wherein the mesh includes a plurality of secondary block meshes connected with the block mesh in a chain between the corner vertex for the corner of the surface and a boundary vertex for a boundary of a second surface of the physical object, wherein the chain corresponds to a chain grid of the grid, wherein the chain grid includes the corner grid point, an end grid point corresponding to the boundary vertex, and a plurality of chain grid points linearly interpolated between the corner grid point and the end grid point.
14 . The non-transitory computer-readable medium of claim 9 , wherein the initial mesh has a plurality of face vertices along boundary edges of the surface between a first surface location and a second surface location, wherein the updated mesh includes face edges extending from respective face vertices, and wherein angles of the face edges relative to the boundary edges are based on a proximity of the respective face vertices to the first surface location or the second surface location.
15 . A system, comprising:
a memory to receive an initial mesh representing a flow domain around a surface of a physical object, wherein the initial mesh has a block mesh for a corner of the surface, wherein the block mesh includes a corner vertex, two boundary vertices, and a border vertex along outer edges of the block mesh, wherein boundary edges of the outer edges connect the two boundary vertices to the corner vertex for boundaries of the flow domain around the corner of the surface, wherein a border edge connects the corner vertex to the border vertex, wherein the initial mesh corresponds to a grid in a parameterized space according to a mapping relationship, and wherein the corner vertex of the initial mesh corresponds to a corner grid point of the grid; and
one or more processors to:
update the corner grid point to obtain an updated grid in the parameterized space according to angles formed by the boundary edges and the border edge, the updated grid being obtained by maintaining fixed in the parameterized space other grid points corresponding to vertices along the outer edges of the block mesh,
determine an updated mesh from the initial mesh according to the updated grid and the mapping relationship to reduce a difference between the angles formed by the boundary edges and the border edge, and
generate a final mesh representing the flow domain for simulating a physical characteristic of the physical object.
16 . The system of claim 15 , wherein the initial mesh includes block-structured embedded meshes within a topology of the flow domain, wherein the topology includes a plurality of topology faces meeting at the corner of the surface, and wherein the border edge is a topology edge extending from the corner vertex between the plurality of topology faces.
17 . The system of claim 15 , wherein the grid includes a block grid corresponding to the block mesh, wherein the block grid has border grid points corresponding to the vertices of the outer edges of the block mesh, wherein the block grid has interior grid points corresponding to interior vertices of the block mesh, and wherein the interior grid points are linearly interpolated between the border grid points.
18 . The system of claim 15 , wherein updating the corner grid point includes moving the corner grid point in the grid without moving the corner vertex in the updated mesh.
19 . The system of claim 15 , wherein the mesh includes a plurality of secondary block meshes connected with the block mesh in a chain between the corner vertex for the corner of the surface and a boundary vertex for a boundary of a second surface of the physical object, wherein the chain corresponds to a chain grid of the grid, wherein the chain grid includes the corner grid point, an end grid point corresponding to the boundary vertex, and a plurality of chain grid points linearly interpolated between the corner grid point and the end grid point.
20 . The system of claim 15 , wherein the initial mesh has a plurality of face vertices along boundary edges of the surface between a first surface location and a second surface location, wherein the updated mesh includes face edges extending from respective face vertices, and wherein angles of the face edges relative to the boundary edges are based on a proximity of the respective face vertices to the first surface location or the second surface location.