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The impact of the Dirichlet boundary conditions on the convergence of the discretized system of nonlinear equations for potential problems

Kucwaj J.

Computer Assisted Methods in Engineering and Science

2016

Vol. 23, no. 1

69--81

The purpose of this paper is the analysis of numerical approaches obtained by describing the Dirichlet boundary conditions on different connected components of the computational domain boundary for potential flow, provided that the domain is a rectangle. The considered problem is a potential flow around an airfoil profile. It is shown that in the case of a rectangular computational domain with two sides perpendicular to the speed direction, the potential function is constant on the connected components of these sides. This allows to state the Dirichlet conditions on the considered parts of the boundary instead of the potential jump on the slice connecting the trail edge with the external boundary. Furthermore, the adaptive remeshing method is applied to the solution of the considered problem.

Numerical investigations of the convergence of a remeshing algorithm on an example of subsonic flow

Kucwaj J.

Computer Assisted Mechanics and Engineering Sciences

2010

Vol. 17, no. 2-3-4

149-160

The main goal of the paper is to analyze convergence of a remeshing scheme evaluated by the author [8] on the example of a potential flow around a profile. It is assumed that flow is stationary, irrotational, inviscid and compressible. The problem is led to solving nonlinear differential equation with additional nonlinear algebraic equation representing the so called Kutta-Joukovsky condition. For adaptation a remeshing scheme is applied. For every adaptation step mesh is generated using grid generator [7], which generates meshes with mesh size function. The mesh size function is modified at every adaptation step by nodal values of the error indicator interpolation. The nonlinear algebraic system of equations obtained from discretizing of the problem, is solved by the application of the Newton-Raphson method.