The authors study a numerical method to approximate the solution of an in-situ combustion model, which is a system of nonlinear parabolic differential equations. The method is based on the nonlinear mixed complementarity problem, a variation of the Newton's method for solving nonlinear systems.
The in-situ combustion model considers the injection of air into a porous medium containing solid fuel. The model consists of a system of two nonlinear parabolic differential equations for the temperature and the molar concentration of the immobile fuel.
The authors describe the finite difference scheme for the in-situ combustion model using the Crank-Nicolson method to approximate the spatial derivatives. They formulate the problem as a mixed complementarity problem and solve it using the FDA-MNCP algorithm.
The authors compare the results of the FDA-MNCP method with the FDA-NCP method from previous work. They analyze the computational time and the relative error for both methods. The results show that the FDA-MNCP method has a slightly higher computational time but similar relative errors compared to the FDA-NCP method, especially as the number of spatial discretization points is increased.
The authors conclude that the FDA-MNCP method is a viable approach for approximating the solution of the in-situ combustion model, with the advantage of providing global convergence compared to the local convergence of the finite difference and Newton's methods.
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by Julio Cesar ... at arxiv.org 10-01-2024
https://arxiv.org/pdf/2409.19502.pdfDeeper Inquiries