A Note on Geometric Conservation Law

guojun liao

Abstract


Moving meshes are desired for field simulations on deforming domains. In addition to conforming to the deforming boundary, moving meshes can also be adapted to fine features of the field solutions such as boundary layers, shock fronts, and material interfaces. The geometric conservation law (GCL) specifies the rate of change in cell volume in terms of the mesh velocity. In the differential form, it is a consistency relation between the mesh velocity and the derivative of the Jacobian determinant of the transformation induced by mesh movements. This law must be enforced in any moving mesh method in order to preserve geometric continuity.
In this work, we treat the GCL as a special case of the transport formula in fluid dynamics. Also, we derive a particularly effective method for moving mesh generation - the deformation method from the same transport formula. At the end, we give a direct proof that the deformation method indeed satisfies the geometric conservation law.

Keywords


Geometric Conservation Law, Transport Formula, Deformation Method

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