Comparison of Different Krylov Subspace Methods Embedded in an Implicit Finite Volume Scheme for the Computation of Viscous and Inviscid Flow Fields on Unstructured Grids

123

SUMMARYA novel implicit cell-vertex ÿnite volume method is described for the solution of the Navier-Stokes equations at high Reynolds numbers. The key idea is the elimination of the pressure term from the momentum equation by multiplying the momentum equation with the unit normal vector to a control volume boundary and integrating thereafter around this boundary. The resulting equations are expressed solely in terms of the velocity components. Thus any di culties with pressure or vorticity boundary conditions are circumvented and the number of primary variables that need to be determined equals the number of space dimensions. The method is applied to both the steady and unsteady two-dimensional lid-driven cavity problem at Reynolds numbers up to 10000. Results are compared with those in the literature and show excellent agreement.

Section: Introductionmentioning

confidence: 99%

A novel fully implicit finite volume method applied to the lid‐driven cavity problem—Part I: High Reynolds number flow calculations

Şahin

Owens

2003

123

“…On the other hand, the temperature equation requires around 20 iterations increasing only modestly with the problem size. The efficiency of the pressure solver can be greatly enhanced introducing more sophisticated techniques based on Newton-Krylov or multi-grid preconditioned solvers [62][63][64][65].…”

Section: Simulations and Discussionmentioning

confidence: 99%

Projection method for flows with large local density gradients: Application to dendritic solidification

Heinrich

Sajja

Felicelli

et al. 2008

SUMMARYNumerical models of solidification including a mushy zone are notoriously inefficient; most of them are based on formulations that require the coupled solution to the velocity components in the momentum equation greatly restricting the range of applicability of the models. Initial attempts at modeling directional solidification in the presence of a developing mushy zone using a projection formulation encountered difficulties once solidification starts, which were traced to the inability of the method to deal with large local density differences in the vicinity of the fluid-mush interface. A modified formulation of the projection method has been developed that maintains the coupling between the body force and the pressure gradient and is presented in this work. This formulation is shown to be robust and extremely efficient; reducing very significantly the necessary storage and the computational time required for the simulation of problems involving very large meshes when compared with previously published data. This is illustrated in this work through its application to simulations involving a Pb-Sn alloy.

“…In order to further investigate the relationship between the CFL number and the residual, we carry out a sensitivity analysis on the function R k given in (9). The derivative of the norm of the density residual R k w.r.t.…”

Section: Sensitivity Analysismentioning

confidence: 99%

On CFL evolution strategies for implicit upwind methods in linearized Euler equations

Bücker

Pollul

Rasch

2008

SUMMARYIn implicit upwind methods for the solution of linearized Euler equations, one of the key issues is to balance large time steps, leading to a fast convergence behavior, and small time steps, needed to sufficiently resolve relevant flow features. A time step is determined by choosing a Courant-FriedrichsLevy (CFL) number in every iteration. A novel CFL evolution strategy is introduced and compared with two existing strategies. Numerical experiments using the adaptive multiscale finite volume solver QUADFLOW demonstrate that all three CFL evolution strategies have their advantages and disadvantages. A fourth strategy aiming at reducing the residual as much as possible in every time step is also examined. Using automatic differentiation, a sensitivity analysis investigating the influence of the CFL number on the residual is carried out confirming that, today, CFL control is still a difficult and open problem.