IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTUREShieh, Y. L.; Lee, J. K.; Tsai, J. H.; Lin, C. A.
doi: 10.1002/(SICI)1097-0363(19970530)24:10<939::AID-FLD524>3.0.CO;2-2pmid: N/A
This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three‐dimensionally evolving jet. Vortical structure developments due to Kelvin–Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single‐programme multiple‐data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet‐oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet‐oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet‐oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939–951, 1997.
USE OF EIGENVALUE TECHNIQUE IN FINITE ELEMENT TIDAL COMPUTATIONSPatil, B. M.; Rao, B. V.
doi: 10.1002/(SICI)1097-0363(19970530)24:10<953::AID-FLD525>3.0.CO;2-Fpmid: N/A
This paper presents the results of some studies on the development and application of a finite element method (FEM) with a closed‐form solution technique for time discretization. The closed‐form solution is based on the eigenvalues/vectors of a coefficient matrix. The method is first applied to the one‐dimensional linearized shallow water equations and then extended to the two‐dimensional shallow water equations. An attempt is made to improve its efficiency by incorporating time splitting and using the closed‐form solution technique only for linear terms. Some case studies of a rectangular channel and harbour are presented to illustrate the satisfactory working of the method. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 953–963, 1997.
SOME VALIDATION OF STANDARD, MODIFIED AND NON‐LINEAR k–ε TURBULENCE MODELSRabbitt, M. J.
doi: 10.1002/(SICI)1097-0363(19970530)24:10<965::AID-FLD526>3.0.CO;2-5pmid: N/A
Standard, modified and non‐linear k–ε: turbulence models are validated against three axisymmetric flow problems—flow through a pipe expansion, flow through a pipe constriction and an impinging jet problem—to underpin knowledge about the solution quality obtained from two‐equation turbulence models. The extended models improve the prediction of turbulence as a flow approaches a stagnation point and the non‐linear model allows for the prediction of anisotropic turbulence. Significantly different values for the non‐linear model coefficients are proposed in comparison with values found in the literature. Nevertheless, current turbulence models are still unable to accurately predict the spreading rate of shear layers. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids, 24: 965–986, 1997.
THE PRESSURE GRADIENT FORCE IN SIGMA‐CO‐ORDINATE OCEAN MODELSSlørdal, Leiv Håvardd
doi: 10.1002/(SICI)1097-0363(19970530)24:10<987::AID-FLD527>3.0.CO;2-Vpmid: N/A
The error in computing the horizontal pressure gradient force near steep topography is investigated in a primitive equation, σ‐co‐ordinate, numerical ocean model (Blumberg and Mellor, in Three ‐Dimensional Coastal Ocean Models, Vol. 4, American Geophysical Union, Washington D.C., 1987, pp. 1–16). By performing simple test experiments where the density field is allowed to vary in both the vertical and the horizontal direction, severe errors are detected in the areas where the isopycnals hit the sloping bottom. An alternative method of computing the pressure force (Stelling and van Kester), Int. j. numer. methods fluids, 18, 915–935 (1994) is adopted, resulting in substantial reduction of the errors. However, a systematic underestimation of the calculated quantities is revealed, leading to erroneous depth‐mean values of the pressure force. In this study a modification of the Stelling and van Kester method is proposed which seems to improve the overall performance of the method. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 987–1017, 1997.
MULTIGRID CONVERGENCE ACCELERATION FOR TURBULENT SUPERSONIC FLOWSGerlinger, P.; Brüggemann, D.
doi: 10.1002/(SICI)1097-0363(19970530)24:10<1019::AID-FLD528>3.0.CO;2-Opmid: N/A
A multigrid convergence acceleration technique has been developed for solving both the Navier–Stokes and turbulence transport equations. For turbulence closure a low‐Reynolds‐number q–ω turbulence model is employed. To enable convergence, the stiff non‐linear turbulent source terms have to be treated in a special way. Further modifications to standard multigrid methods are necessary for the resolution of shock waves in supersonic flows. An implicit LU algorithm is used for numerical time integration. Several ramped duct test cases are presented to demonstrate the improvements in performance of the numerical scheme. Cases with strong shock waves and separation are included. It is shown to be very effective to treat fluid and turbulence equations with the multigrid method. A comparison with experimental data demonstrates the accuracy of the q–ω turbulence closure for the simulation of supersonic flows. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 1019–1035, 1997.
A NON‐LINEAR ADAPTIVE FULL TRI‐TREE MULTIGRID METHOD FOR THE MIXED FINITE ELEMENT FORMULATION OF THE NAVIER–STOKES EQUATIONSWille, Svenøivind
doi: 10.1002/(SICI)1097-0363(19970530)24:10<1037::AID-FLD529>3.0.CO;2-Ppmid: N/A
The full adaptive multigrid method is based on the tri‐tree grid generator. The solution of the Navier–Stokes equations is first found for a low Reynolds number. The velocity boundary conditions are then increased and the grid is adapted to the scaled solution. The scaled solution is then used as a start vector for the multigrid iterations. During the multigrid iterations the grid is first recoarsed a specified number of grid levels. The solution of the Navier–Stokes equations with the multigrid residual as right‐hand side is smoothed in a fixed number of Newton iterations. The linear equation system in the Newton algorithm is solved iteratively by CGSTAB preconditioned by ILU factorization with coupled node fill‐in. The full adaptive multigrid algorithm is demonstr ated for cavity flow. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 1037ndash;1047, 1997.