Pre-conditioning strategies to accelerate the convergence of iterative methods in multiphase flow simulations

A computational bottleneck during the solution to multiphase formulations of the incompressible Navier–Stokes equations is often during the implicit solution of the pressure-correction equation that results from operator-splitting methods. Since density is a coefficient in the pressure-correction equation, large variations or discontinuities among the phase densities greatly increase the condition number of the pressure-correction matrix and retard the convergence of iterative methods employed in its solution. To alleviate this shortcoming, the open-source multiphase code MFiX is interfaced with the linear solver library PETSc. Through an appropriate mapping of matrix and vector data structures between the two software packages, an access to a suite of robust, scalable, solver options in PETSc is obtained. Verification of the implementation is demonstrated through predictions that are identical to those obtained from MFiX’s native solvers for a class of single-phase and multiphase flow problems. For a low Reynolds number, flow over a cylinder case, applying Right Side Block Jacobi Preconditioning to the BiCGSTAB iterative solver in PETSc was faster than MFiX’s native solver. This speed-up increased with higher mesh resolution and for higher-order spatial discretizations. In a fluidized bed simulation, this solver–preconditioner combination resulted in a 25% decrease in solve time compared to MFiX’s native solver.