Abstract
Abstract An explicit finite-difference method has been developed for solving the equations of unsteady laminar natural convection in an arbitrarily shaped cavity. The method developed is an extension of the classical MAC (marker and cell) method to curvilinear quadralateral cells. These cells permit great geometric versatility. The boundary-fitted curvilinear coordinate system is used to generate a coordinate surface coincident with the boundary contours in the physical plane. The conservative form of the momentum equations in primitive variables are transformed to the rectangular computational plane. The MAC technique, formulated in the boundary-fitted coordinates, uses the contravariant velocity components to calculate the mass flux across the cells. A first-order forward difference approximation is used for the time derivative and second-order central difference approximation is used for the space derivatives. The finite-difference form of the continuity equation is satisfied for each cell, which is al...
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