Consistent areas for thermal contact between non-matching unstructured meshes

We describe a thermal contact detection algorithm for projecting a set of three-sided or four-sided polygons onto a second set of three-sided or foursided polygons. The purpose of this algorithm is to provide a geometric foundation for calculating the transfer of heat through contact conductance between unmatched and unstructured meshes. The calculation of projected area is carried out using a series of analytical geometry operations which reduces the calculation to the intersection of coplanar polygons. The result of the contact detection algorithm is a list with the following information: the area common to two polygons, the centroid of the common area, and the location of the centroid in the element parametric coordinates of the original polygons. .The sets of polygons need not be planar; however, polygons will only be projected on polygons for which the dot product of normals is negative. *Member AIAA, Computational Reactive Processes Department TEngineering and Manufacturing Software Department fTherma1 Sciences Department Work supported by the U. S. Department of Energy through Sandia National Laboratories under contract DE-ACOC 94AL85000. This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Introduction Fluid flow and heat transfer calculations in complex geometries are most often simplified by meshing separate components, the complex domain being the composite of simpler parts. We are interested in solution strategies for finite-volume methods where meshes may abut, but do not overlap. In particular, we wish to model the thermal contact resistance problem between two solids using unmatched, unstructured meshes. There is a body of work describing methods for constructing conservative fluxes between nonmatching, structured grids for convective fluid flow. Patched grids have been used by Rai [l] and Walters et al. [2] for the Euler equations of fluid dynamics. Sub-division of control-volume faces in+II uv segments or sub-faces is, d;“moC;strated by Shyy, et al. [3] -.-u YLLVIL) ct 81. \-I, 0,. a,,,4 T.;lolr Fmdamentai to aii these approaches is the calculation of a set of consistent areas between two different meshes. Both Lilek and Shyy describe how to sub-divide opposing surfaces into a set of consistent areas. Walters notes that it is difficult to preserve free stream flow when the patch surfaces are curved, resulting in gaps or overlaps between discrete surfaces. We are not concerned with this issue as of yet because our thermal contact models only deal with the difference in temperature across a gap an not an absolute variable such as pressure. There is also a large body of literature on proximity and contact detection between to solids from the computational mechanics community [6, (c)2000 American Institute of Aeronautics & Astronautics or published with permission of author(s) and/or author(s)’ sponsoring organization. Figure 1: Sub-division of control-volume faces into resistance pairs. 71. These algorithms are more concerned with determining if and where a point on one surface intersects an opposing surface. The TACOSD [8] finite-element heat transfer code implements a master/slave approach to the point/surface contact algorithm. Unfortunately, it is difficult to make any claims about energy conservation across the interface. We think that a surface-surface algorithm is required to assure energy conservation between surfaces. In our paper, we describe a general algorithm for computing the sub-division of consistent areas on unstructured, non-matching meshes. Furthermore, we place no restrictions on surface proximity, allowing us to model the contact conductance between two surfaces separated by a gap. We consider valid the case where two curved surfaces intersect at several points because of discrete faceting. In the following sections, we first describe the algorithm for computing consistent areas. Then, we construct the contact conductance fluxes for both a control-volume finite-element method and a cellcentered finite-volume method.