Alfredo Nicolás¹, Blanca Bermúdez²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.2, pp. 73-84, 2007, DOI:10.3970/cmes.2007.020.073

Abstract 2D viscous incompressible flows are presented from the unsteady Navier-Stokes equations in its velocity-vorticity formulation. The results are obtained using a simple numerical procedure based on a fixed point iterative process to solve the nonlinear elliptic system that results once a second order time discretization is performed. Flows on the un-regularized unit driven cavity problem are reported up to Reynolds numbers Re=4000 to compare them with those reported by other authors, mainly solving the steady problem, and supposed to be correct. Moreover, results are reported for Re = 1000, 4000, 5000, and 10000 to see how their flows look like… More >

J. M. F. Trindade¹, J. C. F. Pereira²

CMES-Computer Modeling in Engineering & Sciences, Vol.20, No.1, pp. 1-10, 2007, DOI:10.3970/cmes.2007.020.001

Abstract In this paper, we discuss the efficiency and speed-up of parallel-in-time calculations of the unsteady incompressible Navier-Stokes equations in a PC-cluster. The parallel-in-time method is based on the alternate use of coarse global sequential solvers with fine local parallel ones in an iterative predictor-corrector fashion. Therefore, the efficiency of parallel calculations is strongly dependent on the number of iterations required for convergence. The one-dimensional scalar transport equation and the two-dimensional incompressible unsteady form of the Navier-Stokes equations were used to conduct numerical experiments to derive some conclusions concerning the accuracy and convergence of the iterative method. A simple performance model… More >

F. Bierbrauer, S.-P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.19, No.1, pp. 1-22, 2007, DOI:10.3970/cmes.2007.019.001

Abstract Recently the use of the one-field formulation in the numerical solution of the Navier-Stokes equations for two-phase incompressible flow has become a very attractive approach in CFD (computational fluid dynamics). While the presence of material discontinuities across fluid interfaces presents some difficulty, it is their combination with a non-solenoidal discontinuous initial velocity field, commonly occurring in the mathematical formulation, that has provided the greatest hindrance in the numerical solution. This paper presents three analytical solutions, the Bounded Creeping Flow, Solenoidal and Conserved Solenoidal Solutions, which are both continuous, incompressible, retain as much of the original mathematical formulation as possible and… More >

H. Lin, S.N. Atluri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.2, No.2, pp. 117-142, 2001, DOI:10.3970/cmes.2001.002.117

Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus^~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems. More >

Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid velocity in a standard projection… More >