BEM for the Analysis of Fluid Flow around MEMS

FACHINOTTI, VÍCTOR; CARDONA, ALBERTO; D'ELÍA, JORGE; PAQUAY, STÉPHANE

Córdoba

Congreso; ENIEF 2007 (XVI Congreso sobre Métodos Numéricos y sus Aplicaciones), MACI 2007 (I Congreso de Matemática Aplicada , Computacional e Industrial).; 2007

Fac. de Cs. Exactas, Físicas y Naturales, Fac. de Matemática, Astronomía y Física, Univ. Nac. de Córdoba.

The boundary element method (BEM) is used in this work for modeling the fluid flow around a vibrating micro-electro-mechanical system (MEMS). Device motion induces flow and, therefore, drag-forces on the surface of the MEMS with a damping effect on MEMS vibration. We assume that the fluid aroundMEMS can be treated as a continuum, and further on, that the fluid can be modeled as incompressible. Under such conditions, met in a large number of MEMS in practice, the fluid flow can be accurately described by Stokes theory of quasi-steady incompressible flow. Further, we will take take into account MEMS deformation effects on fluid flow analysis. Due to the incompressibility constraint, the governing boundary integral equations are ill-conditioned and deserve special treatment. The Mixed-Velocity-Traction Approach and the Fictitious Compressibility Approach are applied to improve the conditioning of the problem. Fast double integration is performed using the collocation method. Self-integrals containing singular kernels are analytically computed over linear triangles. The accuracy of the model is tested using a benchmark problem -- the flow around a sphere moving with constant velocity--, with satisfactory results.