At Los Alamos we are developing a parallel, unstructured-mesh, finite-volume CFD methodology for the simulation of chemically reactive flows in complex geometries. The methodology is embodied in the CHAD (Computational Hydrodynamics for Advanced Design) code. In this report we give an overview of the CHAD numerical methodology and present parallel scaling results for calculations of flows in a four-valve diesel engine

O'Rourke, P.J.

Sahota, M.S.

Zhang, S.

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1a.LA-UR-98-Of$’7~gLos A!amos National Eiboratory is operated by the University of Catifomia for the United States Department of Energy under contract W-7405-ENG-36TITLE A PARALLEL, UNSTRUCTURED-MESHMETHODOLOGY FOR DEVICE-SCALE COMBUSTIONCALCULATIONSAUTHOR(S) P(eter) J. CYRourke,T-3M(anjit) S. Sahota, T-3S(ongwei)Zhang, T-3SUBMllTED TO: Multi-Dimensional Simulation of Engine Internal Flows InternationalConference, IFP, Rueil-A4almaison, France, December 3-4,1998By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce thepublished form of this contribution, or to allow others to do so, for U.S. Government purposes.The Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy.~()~ ~D~~~~ L.. AI.mos National L.~.~a~oryLos Alamo., New Mexico 87545FORM NO. 836 R4ST. NO. 2629 5/81DISCLAIMERThis report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.DISCLAIMERPortions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument./,’. - --, -, ,. -..% ..-. m..= T : -T-TV-T’..-. . . , ,.~. ., .. ~.,.,.. . . . . . . . . . . . . ,1 . .. ., -.. . . . . . . . . ,, ,.. , --—--:-*,,.A PARALLEL, UNSTRUCTURED-MESH METHODOLOGY FORDEVICE-SCALE COMBUSTIONCALCULATIONSP. J. O’ROURKE, S. ZHANG, ANDM. S. SAHOTAGroup T-3, MS B216Los Alamos National LabLos Alamos, NM 87545ABSTRACTAt Los Alamos we are developing a parallel,unstructured-mesh, finite-volume CFDmethodology for the simulation of chemicallyreactive flows in complex geometries. Themethodology is embodied in the CHAD(Computational Hydrodynamics for AdvancedDesign) code. In this report we give an overviewof the CHAD numerical methodology and presentparallel scaling results for calculations of flows in afour-valve diesel engine.INTRODUCTIONComputer simulation of flows in practicalcombustion devices, such as internal combustionengines, is one of the most difilcuk problemsfacing modem computational fluid dynamicsbecause of the number of challenging issues thatmust be addressed before accurate simulations canbe performed. These flows typically involvegeometric complexity (complicated internal flowpassages; moving boundaries, possibly with flowdomain topology changes; and small features, suchas crevices and gaps, whose inclusion can be vitalto correct flow field predictions), physicalcomplexity (turbulence, combustion,multiphase flow, and radiative heat transfer),and numerical challenges (deforming meshes,large density and fluid property variations, thinboundary layers and narrow jets, and coupledEulerian/Lagrangian algorithms). To help meetthese challenges, we at Los Alamos aredeveloping the CHAD code for device-scalecombustion applications.CHAD improves ‘ upon previouscombustion codes developed by Los Alamos(e.g., RICE, APACHE, CONCHAS, andKIVA) in three important respects. First,CHAD uses hybrid unstructured grids inwhich cells in the mesh can be hexahedra orany solid figures-such as prisms, pyramids,or tetrahedra-that can be obtained bycollapsing faces or edges of hexahedra to linesor points. This unstructured mesh capabilitywill enable faster mesh generation in complexgeometries and also improve mesh quality.Second, for computational efficiency CHADuses a variable explicitiimplicit method forcalculating advection [ORourke and Sahota,1998], in addition to implicit treatment ofdiffixion and pressure wave propagationterms. When the computational timestep issmall, a time-accurate explicit advectionscheme is used; when the timestep is large, avariable amount of implicitness is added tomaintiin stability and monotonicity. Thismethodology improves computationalefficiency in calculations of flows withembedded regions, such as boundary layersand jets, with advective time scales that aremuch smaller than problem time scales ofinterest.Perhaps the largest difference betweenCHAD and its predecessors, however, is that it.0.is written to take full advantage of parallelcomputers. Calculations of flotis in p;acticalcombustors are very demanding of computationalresources - requiring high resolution and complexphysical submodels. Current calculations are oftenunder-resolved and use physical submodels thathave known inaccuracies in many applications.Overcoming these deficiencies will require morecomputer power than is available with scalar andvector computers. Parallel and massively parallelplatforms offer the promise of the large increase incomputer power necessary for three-dimensionalcalculations of combustor flows. Because of thevariety of today’s, and undoubtedly tomorrow’s,parallel computer architectures, CHAD is written tobe highly portable on computers having FORTRAN90 compilers. Portability is realized, in part, byplacing all data communication in a small number ofgather/scatter routines in which all machine-dependent coding is isolated. For distributedmemory platforms automatic domain decompositionusing spectral graph partitioning is used to balanceprocessor work load and minimize the cost ofglobal data communication. In this case thegather/scatter routines utilize a message-passinglibrary, written in standard MPI, for global datacommunication.In this paper we first give an overview of theCHAD numerical methodology. We describe themedian mesh control volumes used by the ftite-volume method and illustrate the differencing of ageneric transport equation. Then we present anexample calculation of cold flow in a 4-valve,small-bore diesel engine. Parallel scaling resultsare given for calculations on a multi-processordistributed-memory computer.L CHAD NUMERICALMETHODOLOGYThe CHAD computer code uses a node-centeredfinite volume method to solve the Navier-Stokesequations for a multicomponent mixture of idealgases. When calculating turbulent flows, theequations are supplemented by those of a standardK/&turbulence model. For applications with fuelsprays, these equations can be coupled to equationsfor a vaporizing liquid spray. With minorexceptions, the CHAD equations are those solvedby the KIVA-11code and will not be given here.We also do not describe here the numerical particlemethod for solving the spray equations. Ourintent in this paper is to give an overview ofthe solution method for the gas-phaseequations.A. The Median MeshIn CHAD, conserved variables arefundamentally located at the nodes, or vertices,of a computational mesh that is composed oflogical hexahedra, called elements, whosefaces and edges may degenerate to lines orpoints. The control volumes used toapproximate the integral conservationequations are the so-called “median mesh”control volumes. These are the union of a sub-volume of each of the elements touching thenode. Each element is subdivided into eighthexahedral sub-volumes, one for each node.The sub-volume associated with a node, asillustrated in Fig. 1, has as its vertices thenode itself, the three mid-points of the edgestouching the node, three mid-points of thefaces touching the node, and the centroid of theelement. Figure 2 gives a schematic picture ofthe median mesh control volume surrounding anode in a two-dimensional mesh. We denotethis volume by Vv, where v is a nodal index.741Fig. 1. The subvolume of an element that lies in amedian mesh control volume of node 4. The shadedsurfaces are surfaces of the median mesh controlvolumes.,/ 1“1/-/ wI I noy_4/’y---deVaFig. 2. Median mesh control volume (dashed lines)surrounding node v in a two-dimensional mesh.Fluxes are computed for each face of a medianmesh control volume, and we define one face foreach edge in the mesh. A median-mesh face is theunion of all sub-volume faces that touch theassociated edge. Figure 2 illustrates a median-mesh face in a two-dimensional mesh. Quantitiesassociated with an edge will be denoted bysubscript a. The area projection vector for face awill be denoted by Aa and will be directed outwardfrom the node-v control volume. Note thatalthough Aa is associated with both an edge and anode, we drop the node subscript for brevity. Eachedge is shared by two control volumes, and wedenote by Va the node on the opposite side of facecxfrom the node v under consideration.An edge-based computational procedure is usedin which a list is kept of the edges of all elementsand of the two nodes that bound each edge. Atypical computational sequence involves performingthree DO-loops over the edge list in which we f~stgather necessary information from nodal arrays toedge arrays, second perform calculations using thegathered information (e.g.. calculate fluxes), andthird scatter the calculated information back to nodalarrays while performing an operation (e.g.. addingfluxes).Others have used the control volumes and edge-based data structure described above in conjunctionwith tetrahedral- ~avriplis, 1995] and hybrid-grids [Sehnin, 1993]. Our numerical methoddiffers from previous methods in the means bywhich artificial dissipation is introduced, asdescribed in the next section.B Transport EquationDifferencingCo-located variable schemes, such as that inCHAD, rely on either upwinding, or theintroduction of explicit node coupling, tocontrol alternate node uncoupling problems.CHAD uses a combination of both streamlineupwinding of the advective terms and explicitnode coupling to couple pressures atneighboring nodes. The diffusion terms aredifference by means of a simple and novelscheme that also couples solution variables atneighboring nodes.Transport equation differencing isillustrated by consideration of a genericconservation equation for mass-specificquantity Q:s vwhere p is the gas density, u the gas velocity,points on the surface S of control volume Vmove with velocity v, DQ is the diffisivity,and SQ is a source term. The CHADdifference approximation to this equation is thefollowing:‘z(PD~)a(VQ)~+l A&+l+(sQ)”+’fTn+lVvawhere At is the computational timestep, thesuperscripts denote time levels of numericalapproximation, and the face variables areevaluated by methods we now describe.The quantities pa and Qa are differenceusing the variable explicithplicit methoddetailed in O’Rourke and Sahota [1998]. Asmentioned in the introduction, this schemeemploys a time-accurate explicit scheme when------ .-:): X!XTT —.. ..,0.the local material speed Courant number is less thanone. In this case streamline upwinding is used, andadvected quantities are evaluated at time level tn +At/2, resulting in an advective scheme that issecond-order accurate. When the local Courantnumber is greater than one, a variable amount ofimplicitness is used to maintain stability andmonotonicity. In this latter case, the differencescheme retains second-order spatial accuracy, butbecomes first-order accurate in time.The quantity $a is the exact volume swept outby face ot in moving from its time-n to its time-(n-i-l) position, divided by At, and is positive ifvolume is added to volume Vv by such motion.The cell-face velocity Ua is evaluated by amodified form of the method of Rhie and Chow[1983]:‘+’-+u;:’u,[u :+1+ U::lUa = + Va– z. *:+12 1A;+l[(3)——A“+l 2 2At”n (vp):+l-‘pf+l;Vp::’a P; ‘Pva 1The quantity ya is the rate at which volume wouldbe swept out by face cxif the mesh moved with thefluid velocity; thus in a Lagrangian calculation, inwhich Vv = Uv, in the limit of small At we wouldhave ~a = @u. The pressure gradient terms in Eq.(3) are defined below. These can be interpreted asintroducing a fourth-order pressure node-coupler[0’Rourke and Sahota, in preparation].The cell-face gradient (VQ) ~ is defined byaveraging nodal gradients, and correcting to ensurethat the component of the gradient in the directionof the associated edge, is consistent with thedifference between Qv and QVU: \L( VQV-I-VQva . ~ da ‘4)_F Qva–Qv– 2 )–a lda~whereda=xva–xv .The nodal gradients are defined byVQv=+~Qva; QvAaVaThis cell-face madient amxoximation(5)differsfrom the normal ftite-ele’ient approximation;but it gives equally accurate results in testcalculations we have performed and can beused with an edge-based data structure andhexahedral elements.The system of coupled, nonlinear fmite-difference equations that results from applyingEq. (2) to the gas-phase equations, is solvedby an adaptation of the SIMPLE method, withindividual equations solved by GMRES.Il. EXAMPLE CALCULATION:COLD FLOW IN A 4-VALVEDIESEL ENGINESteady flow is being simulated in an enginein which flow measurements are beingperformed at Sandia National Laboratories andat Ricardo Inc. The engine and its geometryare illustrated in Fig. 3. The engine is of thefour-valve-per-cylinder type, with a swirl typeport provided by Ricardo. Flow through theport and cylinder assembly is driven by aspecified pressure drop. The CHADcalculations are performed with a mesh of200,000 hexahedral elements provided by theUniversity of Wisconsin. The calculationsperformed to date have used the K/s turbulencemodel, although we plan to use sub-grid scaleturbulence models in fidnre calculations.The computational results show theformation of three jets resulting from theinteraction of flows through the two inflowports. These are illustrated in the velocitymagnitude plot of Fig 4. Rotating jets B andC result from flows that enter from each of thetwo ports without interacting with flow fromthe other port. Jet A forms along the center-plane of the engine and results from theinteraction of the flows through the two ports.Because the flows are counter-rotating whenthey meet on the center-plane, there is swirlcancellation and very little rotation associatedwith jet A.,, . .... . . . ...../.. —— .inletH = 158nuuBore= 79.5mmI. . -----I ,>* ......................4H 0001 I , J1 10 100NumberofPnxesstxs!--------. Fig. 5. Parallel speed-up for 4-valve enginecalculation.outletACKNOWLEDGMENTSFig. 3. Illustration of the Sandia, (Rlcardo) engine.Support for this work was provided byU.S. Department of Energy’s Office ofAdvanced Automotive Technologies and Officeof Heavy Vehicle Technologies. We thankMargaret Hubbard for providing figures 3and 4. We also wish to thank Dr. KeithRichards of the University of Wisconsin forsupplying the mesh for the four-valve enginecalculations.cutplan4w%1 N’!i2?91Q7r175; ,_11s3- 331111087.76s.84422.10.393JeiBJetAJetCREFERENCESD. J. Mavriplis, Three-DimensionalMukigrid Reynolds-Averaged Navier-StokesSolver for Unstructured Meshes, AI&4 J. 33,445 (1995).P. J. O’Rourke and M. S. Sahota, AVariable Explicit/Tmplicit Numerical Methodfor Calculating Advection on UnstructuredMeshes, J. Comput. Phys. 143, 312 (1998).P. J. O’Rourke and M. S. Sahota, NO-UTOPL& A Parallel, Implicit Method forCalculating Three-Dimensional Fluid Flows onUnstructured Meshes, in preparation.V. Selmin, The Node-Centered FiniteVolume Approach Bridge between FiniteDifferences and Finite Elements, Comput.Methods in Appl. Mech. Engrg. 102, 107(1993).C. M. Rhie and W. L. Chow, AMA J.21, 1525 (1983).Fig. 4. Velocity magnitude plot in a plane through the twointake valves.The calculations are performed on an SGI Origin2000 computer, and Fig. 5 shows parallel speed-up results for runs on multi-processors of thismachine. It is seen that parallel speed-up is super-Iinear up to four processors, and scales linearlywith processor number above four processors.—.—

A Parallel Unstructured-Mesh Methodology for Device-Scale Combustion Calculations

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