Numerical approximation of the insitu combustion model using the nonlinear mixed complementarity method

TL;DR

This paper presents a numerical approach using the nonlinear mixed complementarity method to approximate solutions for in-situ combustion models, offering improved convergence over traditional methods.

Contribution

It introduces a novel application of the FDA-MNCP method to in-situ combustion modeling, demonstrating its advantages over standard finite difference and Newton methods.

Findings

The method achieves global convergence for the combustion model.

Comparison shows improved stability over traditional methods.

Numerical results validate the effectiveness of the approach.

Abstract

In this work, we will study a numerical method that allows finding an approximation of the exact solution for a in-situ combustion model using the nonlinear mixed complementary method, which is a variation of the Newtons method for solving nonlinear systems based on an implicit finite difference scheme and a nonlinear algorithm mixed complementarity, FDA-MNCP. The method has the advantage of provide a global convergence in relation to the finite difference method and method of Newton that only has local convergence. The theory is applied to model in-situ combustion, which can be rewritten in the form of mixed complementarity also we do a comparison with the FDA-NCP method