Abstract
SummaryA new method to admit large Courant numbers in the numerical simulation of multiphase flow is presented. The governing equations are discretized in time using an adaptive θ‐method. However, the use of implicit discretizations does not guarantee convergence of the nonlinear solver for large Courant numbers. In this work, a double‐fixed point iteration method with backtracking is presented, which improves both convergence and convergence rate. Moreover, acceleration techniques are presented to yield a more robust nonlinear solver with increased effective convergence rate. The new method reduces the computational effort by strengthening the coupling between saturation and velocity, obtaining an efficient backtracking parameter, using a modified version of Anderson's acceleration and adding vanishing artificial diffusion. © 2016 The Authors. International Journal for Numerical Methods in Fluids Published by John Wiley & Sons Ltd.
Highlights
Many porous media flow problems involve highly heterogeneous domains including features such as fractures, which result in a wide range of element sizes and local Courant numbers [1]
The convergence and convergence rate are increased through the use of artificial diffusion that vanishes when the solution has converged. These methods create a very efficient, more robust nonlinear solver that is able to solve for very large Courant numbers using few iterations
The dashed-line (Figure 1 line (A)) is the inner FPMA loop proposed in this subsection, whose computational cost is approximately one-third of a conventional FPMA
Summary
Many porous media flow problems involve highly heterogeneous domains including features such as fractures, which result in a wide range of element sizes and local Courant numbers [1]. Convergence of the solver is never guaranteed when dealing with a nonlinear system of equations Both local and global convergence must be considered. The work is motivated by the fact that the use of a simple FPMA is not enough to achieve convergence when dealing with large local Courant numbers. The convergence rate is increased using acceleration techniques based on Anderson’s method [6]. The convergence and convergence rate are increased through the use of artificial diffusion that vanishes when the solution has converged. These methods create a very efficient, more robust nonlinear solver that is able to solve for very large Courant numbers using few iterations
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