Elliptic grid generation based on Laplace equations and algebraic transformations
- National Aerospace Lab., Amsterdam (Netherlands)
An elliptic grid generation method is presented to generate boundary conforming grids in domains in 2D and 3D physical space and on minimal surfaces and parametrized surfaces in 3D physical space. The elliptic grid generation method is based on the use of a composite mapping. This composite mapping consists of a nonlinear transfinite algebraic transformation and an elliptic transformation. The elliptic transformation is based on the Laplace equations for domains, or on the Laplace-Beltrami equations for surfaces. The algebraic transformation maps the computational space one to-one onto a parameter space. The elliptic transformation maps the parameter space one-to-one onto the domains or surfaces. The composition of these two mapping is a differentiable one-to-one mapping from computational space onto the domains or surfaces and has a nonvanishing Jacobian. This composite mapping defines the grid point distribution in the interior of the domains or surfaces. For domains and minimal surfaces, the composite mapping obeys a nonlinear elliptic Poisson system with control functions completely defined by the algebraic transformation. The solution of the Poisson systems is obtained by Picard iteration and black-box multigrid solvers. For parametrized curved surfaces, it is not necessary to define and solve a nonlinear elliptic Poisson system. Instead a linear elliptic system and an inversion problem is solved to generate the grid in the interior of the surface.
- OSTI ID:
- 121689
- Journal Information:
- Journal of Computational Physics, Vol. 118, Issue 1; Other Information: PBD: Apr 1995
- Country of Publication:
- United States
- Language:
- English
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