
THEMATIC PROGRAMS 

July 4, 2015  
Numerical and Computational Challenges in Science and Engineering Program LECTURE

The objective of reservoir simulation is to predict the complex chemical and physical fluid flows occurring in an underground reservoir sufficiently well so as to be able to optimize the recovery of hydrocarbons. The mathematical models used to describe these fluid flows are coupled systems of nonlinear partial differential equations (PDEs). These systems are characterized by nonlinearities, convection dominance, moving steep fronts, heterogeneity of the porous media, and the enormous sizes of fieldscale applications. Because of these features, solving these systems is very difficult. In this talk, we discuss the compressible fluid flows in an oil reservoir and present an EulerianLagrangian localized adjoint method (ELLAM) to solve the nonlinear system associated with the problem. The ELLAM scheme symmetrizes the governing transport equation, eliminates nonphysical oscillations and/or excessive numerical dispersion. It conserves mass and treats easily boundary conditions in a natural manner. We will present some numerical experiments to illustrate the performance of the ELLAM numerical scheme for fluid flows in porous media. 
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