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... refinement method is for each element in a mesh. Fig.1 is a hexahedral element of a mesh. The conditions (MC) are for tetrahedra only. The following process describes how to use the conditions (MC) to refine a hexahedral element in a given mesh. The refinement process is as follows. 1) Subdivide a hexahedron into five tetrahedra as shown in Fig. 2 and check if l V satisfies the law of mass conservation on all these tetrahedra. If yes, no refinement for the hexahedron is required. If no, go to Step 2. 2) Apply the conditions (MC) to all of the tetrahedra in Fig. 2. If the conditions (MC) are satisfied on these tetrahedra, there is no need to subdivide the hexahedron. Otherwise, ...
Context 2
... element in a given mesh. The refinement process is as follows. 1) Subdivide a hexahedron into five tetrahedra as shown in Fig. 2 and check if l V satisfies the law of mass conservation on all these tetrahedra. If yes, no refinement for the hexahedron is required. If no, go to Step 2. 2) Apply the conditions (MC) to all of the tetrahedra in Fig. 2. If the conditions (MC) are satisfied on these tetrahedra, there is no need to subdivide the hexahedron. Otherwise, we need to subdivide the hexahedron into a number of small hexahedral elements such that the lengths of all sides of the small hexahedral elements are truly reduced (e.g. half). 3) Take the smaller hexahedra in the ...
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Citations
... From a different point of view, an adaptive mesh refinement method based on the law of mass conservation for three-dimensional incompressible or steady flows has been created [10,11]. The corresponding two-dimensional adaptive mesh refinement method was proposed in [8,9]. ...
... We will further investigate the adaptive mesh refinement method in [10,11] with a velocity field that due to a uniform strain and a point vortex [3]. ...
Summary An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained.
