摘要:

AbstractThe time‐dependent Navier–Stokes equations and the energy balance equation for an incompressible, constant property fluid in the Boussinesq approximation are solved by a least‐squares finite element method based on a velocity–pressure–vorticity–temperature–heat‐flux (u–P–ω–T–q) formulation discretized by backward finite differencing in time. The discretization scheme leads to the minimization of the residual in thel2‐norm for each time step. Isoparametric bilinear quadrilateral elements and reduced integration are employed. Three examples, thermally driven cavity flow at Rayleigh numbers up to 106, lid‐driven cavity flow at Reynolds numbers up to 104and flow over a square obstacle at Reynolds number 200, are pres

ISSN:0271-2091    

DOI:10.1002/fld.1650170402

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThe linear stability of numerical solutions to the quasi‐cylindrical equations of motion for swirling flows is investigated. Initial conditions are derived from Batchelor's similarity solution for a trailing line vortex. The stability calculations are performed using a second‐order‐accurate finite‐difference scheme on a staggered grid, with the accuracy of the computed eigenvalues enhanced through Richardson extrapolation. The streamwise development of both viscous and inviscid instability modes is presented. The possible relationship to vortex breakdown is di

ISSN:0271-2091    

DOI:10.1002/fld.1650170403

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractBenchmark problems are solved with the steady incompressible Navier–Stokes equations discretized with a finite volume method in general curvilinear co‐ordinates on a staggered grid. The problems solved are skewed driven cavity problems, recently proposed as non‐orthogonal grid benchmark problems. The system of discretized equations is solved efficiently with a non‐linear multigrid algorithm, in which a robust line smoother is implemented. Furthermore, another benchmark problem is introduced and solved in which a 90° change in grid line directio

ISSN:0271-2091    

DOI:10.1002/fld.1650170404

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents results of an ongoing research program directed towards developing fast and efficient finite element solution algorithms for the simulation of large‐scale flow problems. Two main steps were taken towards achieving this goal. The first step was to employ segregated solution schemes as opposed to the fully coupled solution approach traditionally used in many finite element solution algorithms. The second step was to replace the direct Gaussian elimination linear equation solvers used in the first step with iterative solvers of the conjugate gradient and conjugate residual type. The three segregated solution algorithms developed in step one are first presented and their integrity and relative performance demonstrated by way of a few examples. Next, the four types of iterative solvers (i.e. two options for solving the symmetric pressure type equations and two options for solving the non‐symmetric advection–diffusion type equations resulting from the segregated algorithms) together with the two preconditioning strategies employed in our study are presented. Finally, using examples of practical relevance the paper documents the large gains which result in computational efficiency, over fully coupled solution algorithms, as each of the above two main steps are introduced. It is shown that these gains become increasingly more dramatic as the complexity and size of the problem is incr

ISSN:0271-2091    

DOI:10.1002/fld.1650170405

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY

ISSN:0271-2091    

DOI:10.1002/fld.1650170401

出版商:John Wiley&Sons, Ltd    

年代:1993

数据来源: WILEY