Haar wavelet collocation technique for numerical solution of porous media equations

Abstract

This paper focuses on using efficient Haar wavelet collocation method to nonlinear parabolic differential equations in order to solve steady state pore-scale creeping fluid flow in porous medium, substituting finite Haar series for space derivatives, incontrast forward difference approach is used to estimate the time derivative for porous media equation. These equations has vast number of application in engineering and various other fields such as, in petroleum engineering, there are often situations where fluids are near critical conditions. As oil pressure reduces below the bubble point when gas forms liquid condensations, or when the surface tension become very low i.e, transition from miscibility to immiscibility. To model gas production by pressure decline requires an accurate description of physical mechanism involved in the appearance of the gas bubbles. The observed stability with theoretical convergence assertion, the conservation law of mass and energy are stated. This supports the convergence of the preferred paradigm. A convergent approximation to the porous media equation is obtained by suggested approach. By calculating the maximum error norm and the experimental rate of convergence for various problems, the method efficiency and dependability are demonstrated. The method is accurate, easily applicable, and efficient.