A Comparison of Coupled and Segregated Iterative Solution Technique for Incompressible Swirling Flow

Abstract

SUMMARYIn many popular solution algorithms for the incompressible Navier-Stokes equations the coupling between the momentum equations is neglected when the linearized momentum equations are solved to update the velocities. This is known to lead to poor convergence in highly swirling flows when coupling between the radial and tangential momentum equations is strong. Here we propose a coupled solution algorithm in which the linearized momentum and continuity equations are solved simultaneously.

A coupled finite volume solver for the solution of incompressible flows on unstructured grids

“…Because the cost per iteration is higher for the coupled solver, it is more meaningful to compare the CPU time consumed by both solvers. Results in Table 3 indicate that as the grid size increases from 10 4 to 3 Â 10 5 quadrilateral (triangular) control volumes, the corresponding ratio of the CPU time needed by the segregated solver to the CPU time required by the coupled algorithm increases from 13 to 115 (13-104), 18 to 71 (8-58), 4 to 31 (3-33), 8 to 56 (6-54), 8 to 22 (6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25), and 5 to 38 for the above problems. This represents a tremendous savings as the total time required by the coupled approach to solve all problems on the coarsest and densest quadrilateral (triangular) grids used are 209.6 and 11660.1 (339.7 and 12849.3) seconds while the times required by the segregated method are 1844.89 and 525911.74 (2113.11 and 564206) seconds with the average S/C ratio varying from 8.8 to 45.1 (6.22-43.9).…”

“…This renewed interest in the development of coupled solvers [4,5] is due to the tremendous increase in computer memory and to the convergence problem experienced by segregated solvers when used with dense computational meshes [6]. Even though the convergence issue has been addressed successfully through multigrid, parallel processing, and domain decomposition the convergence issue has not been directly resolved.…”

“…Since no pressure equation is derived, zeros are present in the main diagonal of the discretized continuity equation leading to an ill conditioned system of equations. This problem has been addressed, with various degrees of success, through the use of pre-conditioning [6], penalty formulations [21], or by algebraic manipulations [22].…”

Theoretical study of electrolyte transport in nanofiltration membranes with constant surface potential/charge density

“…The stationary problem was solved iteratively by two methods in finite volume formulation [32]. The first one is the Coupled scheme [33], which solves the pressure-based momentum and continuity equations together. The second is the SIMPLEC scheme [34], where the momentum equation is segregated from continuity equation, from which the Poisson equation for pressure is derived and solved to obtain the velocity correction.…”

Spurious transients of projection methods in microflow simulations

“…A detailed study of the convergence of the time discretization is conducted, which serves both as verification of the implementation and as direct comparison of the different variants in a low-inertia flow. A similar study involving monolithic and segregated methods for incompressible fluid flows was presented by Elman [30], though in that paper the goal was to investigate the performance of preconditioning strategies (see also [31]). …”