Bi-CGSTAB method with red-black Gauss-Seidel preconditioner applied to the hermite collocation discretization of subsurface multiphase flow and transport problems

The solution of the Hermite collocation discretization of the partial differential equations that govern subsurface multiphase flow and contaminant transport requires considerable computational effort. To minimize this burden, we solve these equations using the Bi-CGSTAB method with a red-black Gauss-Seidel preconditioning matrix. We find that our method of solution is virtually always much faster than the commonly used GMRES method with ILU preconditioning. In addition, our choice of preconditioner allows easy implementation on a parallel processing computer.