Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Computations of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code
Computations of Nonlinear Turbulent Free Surface Flows Using the Parallel Uncle Code
Pages 805-819
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From page 805... ...
tem The mmericcl reproach uses She mod tea artfficicl compressibility formulation The governing equations are discretized using c to nite vol me approach where the m mericcl flw.es et cell interfaces are obtained using Roe's inviscid flux averages coupled wish m L er's MUSCL formulation for higher order flux extmpolction Viscous flw.es are avenged using central dffferencmg Time is discretized implicitly using She first order Euler backward differencing The resulting non I near algebraic eq onions are solved using the discreti:D:d Newton relaxation AND) cpproah with sym mehiccl Gauss Seidel weeps To speedup the solution process c parallel implementation of the m mericcl clgorithm duct uses h HI for message pcssmg is used in order to acelemte the solution Converges e process c multilevel cpproah coupled with the t additional multig id reproach is taken The resulting algorithm has beer applied to various ship geometries ad comparisons with the sequential code solutions Ed experimental resuits are presented The results show duct the parallel version of the f ee surfae UNCLE code sccnrsteh reproduces these earlier results INTRODUCTION Nonlinear, turbulent free surfa flows represent m import mt cuss of problems wish immediate mrval applications e peciclly when mch flows occur in the vicinity of 9 body These problems are ve y challenging from c Computational Fluid Dynamical pomt of view m that Hey dorm Ed c ve y robust m mericcl algorithm, very large computational resources Ed ve y Urge limo mts of computing time More import Fitly, in cddition to robust ess, She CF algorithm must model the correct physics The original UNCLE ( for UN teddy Computation of fieLd Equations )
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From page 806... ...
multig id clgorithm is used to a elemte the convergence The free surfae kinemtric bo mdary condition is solved using the same cpproah Since She present cpproah falls aider the category of front tracking methods, it is necessary to regenercte She f ee surfae ad the mderlymg g id et etch time tep The free smfae is ass med to be of the form y = Y(t;, t,'t) where to attd Care surfae curvilinear coordinates ad ~ denotes time Thus, in solvmg the kinematic bo mdary condition one obtains m increment Ay et every pomt on the free surfa for a increment At m time Using the Ay's the new free smfae position is obtained ad the flow g id is updated using c btckg o mdg id The parallel code was verified by mming the same cases es She sequential code ad the re mlts w re compared with experiments The majority of She results show are for Series 60 Cal = 0 6 ad Model 5415 The flow parameters for Series 60 Cs = 0 6 were specifled by the experiments to be es follows: c Froude m mber of 0 316 md c Rey olds m mbff of 4 2 X lOs For Model 5415, the Froude m mber was given es 0 2756 ad She R y olds m mber es 12 02 X lot Some of She prffUrSO y works m free surfae flow computations ctout surfae ships w re performed by Miyata ad Nishimurc (1985)
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From page 807... ...
and using the so-called partial transformation in which the vectors and tensors that appear within the divergence operator are expressed with respect to the underlying Cartesian coordinates whereas the divergence operator itself is expressed in terms of the curvilinear coordinates, one can obtain the so-called numerical vector form which is as follows: dQ + dF + dG + dH + dFv + dGv + dHv O (4) where, lines ~ increasing from the bottom boundary to the top ~ S lines ~ increasing from the Fv = ,: body to the outer side boundary ~ mensional grid velocity vector, a= tUo/L, is the non-dimensional time, c, is the Stokes tensor and P' = P + x/Fr2 where p = (p*
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From page 808... ...
mtrodue the curvilmear coordim~tesoncflctsmfae(ie x phne) whffecsthepr sent formoktion inhoduces them on the atual free surfae Any book on differ nticl geometry, Warsi (1998)
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From page 809... ...
A efficient way of implementmg ther exat conditions is outlined in Beddhu et cl (1997) How v r, in the present st dy e at dynamic bo mdary conditions are not used Smce the exterm~l tmgentiel shesses are neglected md only the etm ospheric pr ssure is considered in 6he nommel shess component md elso smce the g id near the free surfae is not fme enough to resolv 6he weak surfae hyer, the dynamic bo mdary condition hes been epproximately implemented by m my eubhors for computing ship rehted flows For exemple, commonly used epproximate conditions ere 'lu = 0; C]
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From page 810... ...
Update the bo mdary conditions on She flow varictles on all surfaces 3) Use the kinematic condition to find She new position of She free surfae 4)
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The linearized approximations at each time step are solved using a block Jacobi symmetric Gauss-Seidel ~ BJ-SGS ~ relaxation procedure that involves communication at each sub-iteration level. The sequencing of forward and backward sweeps interspersed with data exchange is shown in Figure 4.
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From page 812... ...
Repeat steps 1~3 for ~ times at the same time level, using Oh as the new approximation to Qn+~. In the above procedure, J\E is the number of Newton sub-iterations for the fine grid and coarser grids, and ~ is the number of multigrid cycles implemented at each time step.
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From page 813... ...
0.010 0.000 -0.010 -0.020 -0.6 -0.4 -0.2 0.0 0.2 x 0.4 Fig. 8 Hull Profile Comparisons for Wigley Hull Fr= 0.289; Re= 3300000 Expt Sequential - Parallel The free surface version of the parallel UNCLE code described in the earlier sections was used to compute the free surface flow fields around three popular hulls: (1)
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From page 814... ...
Computed results using the sequential UNCLE code for the Wigley hull were reported in Beddhu et al (1998a)
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In Fig. 12, comparison of the overall wave contours between experiment and computation using the parallel UNCLE code is shown.
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From page 816... ...
Fig. 19 Comparison of Stern Wave Contours for Model 5415 Fr = 0.2756; Re = 12.02 x 106 · Expt Sequential - Parallel The free surface version of the parallel UNCLE code was designed to be a production mode code that is fast, robust and reliable.
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From page 817... ...
R "Parcllel Solution of Viscous incompressible Flow on Multi Block Shuctured Gkids Using MPI", Parcllel Comcutatiomrl Fluid Dvnamics Imclementations mdRemltsusm~Pcmllel Comcuters, Eds: S Tcylor, A Ecff, J Perisux md N Sctafi~cc, Eisviff Science, B V, Amsterdam, 1996, pp 601608 ParJccjakshm, R, "Pcmllel Solution of Unstecdy Incompress~ble Flow Using Multi Block Structmed Grids," Ph D Disse tation, Mississippi State University,Dec 1997 ParJccjakshm, R, Tcylor, L K, Jimg, M Y, R motig e, M G, Briley, W R md Whiffield, D L, "Pcmllel Simoktions for Conhol Smface Induced Submarine M meuvers," A AA Pcper 2000 0962, 2000 Olivieri, A, Pclmi, M, md Pem~, R, "Studio sperimentale del campo fluidodirumico mtorno cd unc care
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From page 818... ...
3, Nos 1 4, pp 393 399, 1992 m L er, B "Towards fhe Ultimate Conservation Dffference Scheme V, A Second O der Sequel to G dunov's Medhod," Jourm~l of Comcutatiorurl Phvsics, Vol 32, 1979, pp 101 136 Whiffield, D L md Tcylor, L K, "Discretied Newton R laxation Solution of High R solution Flux Dffference Split Schffmes,"AlAA 91 1539, June 1991 Whiffield, D L md Tcylor, L K, 'N mericcl Solution of fhe Two Dimensiom~l Time D pendent ~compressible Enler Eq mions," MSSU E RS ERC 93 14, Mississippi State University, Mississippi MS 39762 April, 1994 Whiffield, D L md Tcylor, L K, "Vari mts of c Two Level Medhod for fhe Approximate N mericcl Solution of Field Simulation Equations," MSSU E RS ERC 98 09, Mississippi State Uni ffsity, Mississippi MS 39762 July, 1998 Warsi, Z U
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From page 819... ...
DISCUSSION S Cordier Bassin d'Essais des Carenes, France he use of gods fitted to She free surface has limes when s~muhtmg non-linear tree su face flows (braying Ed jets for example)
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