RP-Department of Mathematics
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Browsing RP-Department of Mathematics by Author "Gatheri, F. K."
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Item The method of the false transient for the solution of coupled elliptic equations(Elsevier, 1973-08-04) Gatheri, F. K.A method for the numerical solution of a system of coupled, nonlinear elliptic partial differential equations is described, and the application of the method to the equations governing steady, laminar natural convection is presented. The essential feature of the method is the conversion of the equations to a parabolic form by the addition of false time derivatives, thus, enabling a marching solution, equivalent to a single iterative procedure, to be used. The method is evaluated by applying it to a well known two-dimensional problem and some examples of its use in three dimensions are given.Item The Method of Variable False Tranelents for the Solution of Coupled Elliptic Equations(Faculty of Science Kenyatta University, 2005) Gatheri, F. K.A method for the numerical solution of coupled, non-linear elliptic, partial differential equation is described. The essential feature of the formulation is the use of different false transient factors in different flow regions. In regions where velocity gradients are high, small time steps are required so that small false transient factor are used, elsewhere large time steps and false transients factors are employed. The number of iteration required for convergence was significantly reduced when compared with the conventional method. The effectiveness of the method is demonstrated by applying it to the problem of natural convection in a three dimensional enclosure heated and cooled on one wall.Item The Use of Mesh Generation Function for the Solution of Natural Convection Problems(Faculty of Science Kenyatta University, 2005) Gatheri, F. K.A mesh generation procedure for the solution of coupled, non-linear, partial differential equation is described. The essence of the procedure is the use of a grid generating function, which results in a strong refinement along the walls. In viscous fluid flow, the problem arises where the solution varies rapidly over a small part of the domain but over the rest of the domain changes very slowly. At very large Reynolds number, viscous fluid flow pattern changes rapidly in narrow boundary layers close to walls where the fluid is brought to rest. In such convection dominated flows it is desirable to concentrate more mesh points in certain regions of the cavity. This is in order to place more mesh points within areas of steep velocity gradients. The effectiveness of the procedure is demonstrated by applying it to the problem of turbulent natural convection in an enclosure with colliding boundary layers.