Date of Award
Master of Science (MS)
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 impede 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, the access to a suite of robust, scalable, solver options in PETSc is obtained.
Verification of the implementation of MFiX-PETSc is demonstrated through predictions that are identical to those obtained from MFiXâs native solvers for a simple heat conduction case with a well-known solution. After verifying the framework, several cases were tested with MFiX-PETSc to analyze the performance of various solver and preconditioner combinations.
For a low Reynolds number, flow over a cylinder case, applying right-side Block Jacobi preconditioning to the BiCGSTAB iterative solver in MFiX-PETSc was 28-40% faster than MFiXâs native solver at the finest mesh resolution. Similarly, the left-side Block Jacobi
preconditioner in MFiX-PETSc was 27â46% faster for the same fine meshing. Further assessments of these preconditioning options were then made for a fluidized bed problem involving different bed geometries, convergence tolerances, material densities, and inlet velocities.
For a three-dimensional geometry with uniform meshing, native MFiX was faster than MFiX-PETSc for each simulation. The difference in speed was minimized when a low density fluidization material (polypropylene) was used along with a higher order discretization scheme. With these settings, MFiX-PETSc was only 2-6% slower than native MFiX when right-side Block Jacobi preconditioning was employed. The fluidized bed was then represented by a two-dimensional geometry with fine meshing towards the center. When this bed was filled with glass beads, right-side Block Jacobi was 28% faster than MFiXâs native solver, which was the largest speedup encountered throughout this 2D case.
Clarke, Lauren, "Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times" (2018). Theses and Dissertations. 2189.