Abstract

In this work, a hierarchical variant of a boundary element method and its use in Stokes flow around three-dimensional rigid bodies in steady regime is presented. The proposal is based on the descending hierarchical low-order and self-adaptive algorithm of Barnes-Hut, and it is used in conjunction with an indirect boundary integral formulation of second class, whose source term is a function of the undisturbed velocity. The solution field is the double layer surface density, which is modified in order to complete the eigenvalue spectrum of the integral operator. In this way, the rigid modes are eliminated and both a non-zero force and a non-null torque on the body could be calculated. The elements are low order flat triangles, and an iterative solution by generalized minimal residual (GMRES) is used. Numerical examples include cases with analytical solutions, bodies with edges and vertices, or with intricate shapes. The main advantage of the presented technique is the possibility of considering a greater number of degrees of freedom regarding traditional collocation methods, due to the decreased demand of main memory and the reduction in the computation times.

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This work presents the results of the analysis of the one-dimensional advective diffusion equation from the Boundary Element Method. The developed formulation use a time independente fundamental solution and a transformation of the domain integral into weighted boundary values, which avoids the use of reciprocidy or discretization techniques in cells for the domain integrals. Accurate results were obtained for the boundary variables in two cases steady state heat transfer and these results allowed a particular study on the advective velocity, which pointed an expression for calculation when the variables of temperature and heat flux were known, which expression is presented at the end of the work.

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