Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:A2L-A

Session:

Number:38

Multiscale cut-cell closures for hybrid computational architectures

Sorin Mitran,  

pp.38-38

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.38

PDF download (260.8KB)

Cut-cell methods [1]-[4] solve partial differential equations in domains with complex geometry by ”cuts” within the cells of a background Cartesian mesh. The method has been successfully applied to Euler flow [1], [2], shallow-water flow [4], and extended to include effects from moving boundaries.
A persistent difficulty in cut-cell methods is the formation of small-volume cuts that severely limit allowable CFL number in explicit computations or lead to increased stiffness in implicit systems. Furthermore, there is significant interest in including additional physical effects at an interface as in the case of multiphase flow. This talk presents an approach that solves both the above problems by a multiscale approach suited to current developments in computer architecture. The base cut-cell method is solved on central processing units (CPUs). Fluxes and boundary conditions on cut cells are determined by a kinetic models running concurrently on graphics processing units (GPUs) or alternative vectorized coprocessors. The kinetic models considered are lattice Boltzmann methods for Newtonian fluids and lattice Fokker-Planck methods for non-Newtonian methods. The concurrent kinetic models solved on GPUs envelop the regular Cartesian cells within the computational zone with a buffer zone of cut-cells. The overall computation proceeds at the CFL number set by stability considerations on the background Cartesian mesh.

[1] M. Berger, R. LeVeque, An Adaptive Cartesian Mesh Algorithm for the Euler Equations in Arbitrary Geometries, AIAA paper 89-1930-CP, 1989.

[2] J. Quirk, An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies, Comput. Fluids 23 (1) (1994) 125142.

[3] G. Yang, D. Causon, D. Ingram, Calculation of compressible flows about complex moving geometries using a 3D Cartesian cut cell method, Int. J. Numer. Methods Fluids 33 (2000) 11211151.

[4] D. Causon, D. Ingram, C. Mingham, G. Yang, R. Pearson, Calculation of shallow water flows using a Cartesian cut cell approach, Adv. Water Resour. 23 (2000) 545562.