Domain composition methods for combining geometric and continuum field models

Jordan Jay Cox, Purdue University

Abstract

Numerical methods for solving continuum problems decompose a global domain into simpler, non-overlapping sub-domains over which the continuum equations can be posed. The common boundaries of these sub-domains require a specification of compatibility and continuity for the solution to be globally continuous. Many numerical methods take advantage of the implicit compatibility and continuity specifications obtained when solution points or nodes are shared and the basis functions are equivalent. This requires that globally compatible meshes be constructed that approximate the global shape of the part. A new method for specifying compatibility and continuity that takes advantage of the geometric overlaps common in geometric modeling is presented. The method involves posing continuum equations on the sub-domains, some of which may be overlapping, as if the sub-domains are independent. When these sub-domains are combined through set operations to form a global geometry, there are redundant statements of the continuum equations where the sub-domains overlap. Constraints are applied to force the redundant solutions within an overlap to be equivalent. When the overlapped solutions are equivalent the derivatives or fluxes are also equivalent, thus producing the continuity and compatibility desired between the two sub-domains. This technique eliminates the need to produce a globally compatible mesh. It provides a close correlation between the local shape of a part and the continuum equations. These methods allow the designer to better explore the relationship between shape and function.

Degree

Ph.D.

Advisors

Anderson, Purdue University.

Subject Area

Mechanical engineering|Mathematics|Computer science

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