Parallelization of the Euler Equations on Unstructured Grids

摘要: D.... Diagonal block in the matrix problem Several different time-integration algorithms for g Euler implicit time integration equations are investigated on two distributede... Specific internal energy memory parallel computers using an explicit messageo stagnation passing paradigm: these classic Explicit, f... Flux vector four-stage Jameson-style Runge-Kutta, Block Jacobi, -f««m --•••• -Numerical flux Gauss-Seidel, and Symmetric /,/~.... ........ Upwind vectors Gauss-Seidel. A finite-volume formulation is used //> Fraction of that parallelizable spatial discretization physical domain. Both h0.. ....Specific enthalpy twoand three-dimensional test cases evaluated L Lower-triangular inner against five reference solutions to demonstrate accuracy arising fundamental sequential algorithms. Speedup l Inner iteration number; stage number efficiency issues pertaining various time-integraJameson-style Runge-Kutta tion addressed each computer system. ,„„ „„„ inegraion „ , . ., t • V>i i LHS,RHS...... Left-hand side, right-hand side Of considered, ° solicit! on. Gauss-Seidel has overall best performance. It also m _____ Number stages Rungedemonstrated as sole Kutta means evaluating performance algorithm often # compute nodes a given leads erroneous conclusions; clock needed run; quantity associated with cell's solve much better indicator immediate neighbor general method extending one-dih Unit normal face mensional limiter formulations unstructured case p Thermodynamic pressure briefly discussed applied Van Albada's Q.. ....Conservative variable vector, well Roe's Superbee limiter. Solutions conver0 = I o \ gence histories two-dimensional supersonic ramp ^ ' "^ limiters presented along &• & "••-States left 8 sides computations Earth Jesperson respectively Venkatakrishnan — Albada per esiua vec or rf..r., .Position centroid wrtacell formance similar s. J XT S..... Surface domain integration; area Nomenclature A, A' .........Flux jacobian matrices at > SGS B Baseline tB Mawxed convergence baseline c heat constant fo Measured Anodes -c u * to/. .User-specified tolerance cv......... ......... volume r *[ =-: ———— TT ,, This paper declared work U. S. Government, v __ Upper-triangular not subject copyright protection United integ^ation «.... ..Generic scalar Aerospace Engineer, Advanced Aerodynamics .-, f .. T^ >. j ^0-Mr.r.A 11^/00 r>u 1101 Cartesian components ot velocity Branch, Code 432100A, M/S 3, Bldg. 2187. Senior y Flow Member AIAA. Coefficient fPresident. 1872 Pratt Drive, Suite 1275. Associate 6 Fellow l/(m+l-l)