A dual mesh control domain method for the solution of nonlinear Poisson's equation and the Navier-Stokes equations for incompressible fluids
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abstract
In this study, the dual mesh control domain method, which employs the finite element approximation of the primary variables and the finite volume idea of satisfying the governing equations over a control domain, is used for the numerical solution of the NavierStokes equations governing the flows of viscous incompressible fluids using the penalty function formulation for two-dimensional analysis. The primal mesh is the mesh of finite elements used to interpolate the velocity field, while the dual mesh of control domains is used to satisfy the integral form of the NavierStokes equations, and thus, the method shares certain desirable features of the two popular methods. Numerical examples involving nonlinear Poissons equation and the NavierStokes equations are presented to illustrate the methodology and accuracy compared to the finite element and finite volume solutions, the latter depending on the scheme used to solve the discretized equations.
