STABILITY ANALYSIS AND NUMERICAL-SIMULATION OF 1-D AND 2-D RADIAL FLOW TOWARDS AN OIL-WELL

The radial flow of oil towards a well in one and two dimensions is mod eled by a family of finite difference schemes. This family depends on one parameter theta, 0 less than or equal to theta less than or equal to 1. The stability of the proposed schemes is analyzed applying the m atrix method, which takes into account boundary conditions. Particular ly, in the 2-D case, an ''almost pentadiagonal'' matrix is obtained ch oosing an appropriate order of equations and unknowns. We prove that t his matrix may be symmetrized by a similarity transformation. Therefor e, studying bounds for the corresponding eigenvalues, unconditional st ability is found for theta greater than or equal to 1/2 and stability restrictions are established for theta < 1/2. Numerical simulations ar e presented using the BSOR (Block Successive Over Relaxation) method t o solve the resulting system of linear equations. The finite differenc e solution has perfectly reproduced the analytical solution of a simpl ified 1-D model.