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Development of least-square-based two-dimensional finite difference schemes and their application to simulate natural convection in a cavity. (English) Zbl 1033.76039
Summary: We present two-dimensional mesh-free finite difference schemes for solving incompressible viscous flows. The method is based on the use of a weighted least-square approximation procedure together with Taylor series expansion of unknown functions. Discretization error for derivatives is investigated analytically on uniform mesh, and convergence property of the method is numerically tested. The role of the weighting function in the method is studied. Neumann-type boundary condition is treated by applying locally orthogonal boundary grids. Application to a natural convection in cavity is demonstrated on three different types of point distribution.

MSC:
76M20 Finite difference methods applied to problems in fluid mechanics
76R10 Free convection
80A20 Heat and mass transfer, heat flow (MSC2010)
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