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日本航空宇宙学会北部支部2006年講演会および第7回再使用型宇宙推進系シンポジウム(2006年3月9-10日), 仙台, 資料番号: ARDS05482000, レポート番号: G-4

平成17年度宇宙科学情報解析センターシンポジウム（2005年11月10日. 宇宙航空研究開発機構宇宙科学研究本部(JAXA)(ISAS)）, 相模原市, 神奈川県, 2005 PLAIN Center Symposium (Space Science Informatics Symposium FY2005) (November 10, 2005. Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency (JAXA)(ISAS)), Sagamihara, Kanagawa Japan, 資料番号: SA6000109001

ITBL is an abbreviation of IT-Based Laboratory named by Dr. Himeno of Riken. Which essence is virtual research environment constructed with resources widely distributed on network such as computing resources, software resources including databases, human resources and knowledge. ITBL will realize such environment as a system which any users can access to resources anytime from anywhere. Grid technology is necessary to construct virtual environment. However only to share hardware resources is not ITBL's objective, but to share knowledge and to create such remote collaborative system is more important issue. In this view point application oriented PSE (Problem Solving Environment) supposed to widely utilize through internet is another important theme. Grid technology has been accumulated and is now under developing mainly by information technology researchers which can be recognized as seeds technology to construct virtual environment. From viewpoint of utilizing such environment approaches from application researches, that is standpoint from needs, will be required. So to realize ITBL, collaboration among information technology researchers and application researchers is essentially important. This article is contributed to these points., 資料番号: AA0045948008, レポート番号: NAL SP-57

In this paper, a generalized interpolation-based lattice Boltzmann method (GILBM) is introduced. The standard lattice Boltzmann equation is transformed into generalized coordinates using metrics. The advection term of the transformed equation is discretized with sufficient spatial accuracy to suppress the numerical dissipation. Additionally, a wall boundary condition suitable for body-fitted grids and a non-reflecting outer boundary condition are introduced. With the present method, the flow around a complex geometry can be solved using structured grids. The three examples of, the cavity flow, the flow around a circular cylinder, and the flow around an airfoil are shown as validation of the method to a wide range of Reynolds number. The present results show good quantitative and qualitative agreement with other computational studies., 資料番号: AA0045948047, レポート番号: NAL SP-57

Recent years, Lattice Boltzmann Method (LBM) has become one of the promising schemes for incompressible flow simulation. Since LBM is based on Cellar Automaton, its original version is formulated on uniform homogenous mesh system. Applying general coordinate system enables allows flow computation around arbitrary body shape with sufficient accuracy in the boundary layer. In this present study, flow around cylinder was simulated for wide range of Reynolds number. Computational results show that the present LBM code can successfully predict drop in the drag coefficient at Reynolds number 10(exp 5) to 10(exp 6), which is known as 'drag crisis' from the experimental data., 資料番号: AA0032819035, レポート番号: NAL SP-53

航空宇宙技術研究所 7-9 Jun. 2000 東京 日本, National Aerospace Laboratory 7-9 Jun. 2000 Tokyo Japan, 本論文では、航空機エンジン、船舶、発電所のターボ機械の空力設計技術者のために効率的な技術環境を実現する翼列設計用のCFD(計算流体力学)プラットフォームについて解説した。プラットフォームをネットワークで接続したPC、ワークステーション(WS)、スーパコンピュータから構成した。このプラットフォームでは設計者が計算グリッドを生成したり、流体計算をしたり、計算結果を解析、視覚化する際に、その操作が容易になる様、CFDプログラムをこれらのコンピュータで運用するためのグラフィックユーザインタフェースを提供した。また、翼列の幾何学的形状のようなデータや、計算した流体のデータの様に空力性能を比較したり、翼列の設計を評価するのに必要なデータをデータベースに保存したり、参照したりする機能も保持した。本稿では、2次元の翼列のために開発したプラットフォームのプロトタイプを紹介した。多段ターボ機械のための流体解法コードも並列計算ライブラリとともに開発し、このプラットフォームに取り込んだ。, The present paper shows a CFD (Computational Fluid Dynamics) platform for blade rows, which realize efficient engineering environment for aerodynamic designers of turbomachine for aircraft engines, ships and electric power plants. The platform consists of PCs, WSs (Workstations) and supercomputers on network. It provides graphic user interfaces on these computers to control the CFD programs, so that the designers can operate very easily their tasks such as generating the computational grids, calculating the flow, and analyzing/visualizing the computed results. It also has the functions to save/restore in the database such data as geometric profiles of blade rows, computed data of the flow, which data are necessary to compare the aerodynamic performance and estimate the design of blade row. In this paper, a prototype platform is demonstrated, which has been developed by the authors for two-dimensional blade rows. A flow solver for a multi-stage turbomachine is also developed with parallel computing library and incorporated in this platform., 資料番号: AA0028635042, レポート番号: NAL SP-46

航空宇宙技術研究所 7-9 Jun. 1995 東京 日本, National Aerospace Laboratory 7-9 Jun. 1995 Tokyo Japan, 計算流体力学(CFD)は航空機や宇宙機の設計・開発にますます重要な役割を担うようになった。CFD技法を用いて航空宇宙機の設計コストを大幅に減少できることは良く知られている。最新のCFDでは航空宇宙機の複雑化した現実的な形態の計算が扱われる。従来の共有メモリ型計算機のコストパフォーマンスの限界を考慮して、超並列計算機(MPP)アーキテクチャの導入・利用を進める必要がある。ここでは、Intel社のParagon XP/S25(336ノード)によるNAL(航技研)のMPPシステムにおける、メッセージ交換インタフェース(MPI)を用いたCFD計算を紹介する。2次元Euler方程式に基づくTVDスキームコードによるMIMD(多重データ多重命令)型計算に焦点を絞って討議した。高次スキームでは5点差分を用いた。90度コーナー周りの衝撃波の回折数値シミュレーションを実行した。計算領域はMPPコードに適合させ正規小領域に分割し、それぞれの領域に見合った局所的な境界条件を考慮した。本計算では局所領域を9タイプに類別し、各小領域はどれかのタイプに属するようにした。境界値は付加領域の2メッシュを異種形態のMPIを用いて相互変換する。進行する波面はMIMD型計算におけるMPIの適用によって可視化できる。空間複合化に対する計算効率はメッシュサイズとノード数を変えることにより討議できることになる。, The Computational Fluid Dynamics (CFD) has an increasingly important role in the design and development of aeronautical and space vehicles. It is well known the costs of the design of aerospace vehicles can be greatly reduced by using the CFD technique. Recent trend of CFD is the computations around more complex and realistic configurations. Considering the limitation of the cost performance of single processor shared memory machine, progress is being made in the direction to the application of Massively Parallel Processor (MPP) architectures. In this presentation, the CFD calculation is introduced using the Message Passing Interface (MPI) in the NAL MPP system, Intel Paragon XP/S25 (336 nodes). Discussions are focused on the MIMD (Multiple Instruction of Multiple Data) type treatment for the Total Variation Diminishing (TVD) scheme code of two dimensional Euler equations. The numerical higher order scheme is the five points difference one. The numerical simulations of shock diffraction around a 90 deg corner are performed. The numerical region is divided into regular small regions which correspond to MPP nodes: each node takes care of local numerical calculations with different boundary conditions. In the present situation, the local region is categorized into nine types. Any small region belongs to one of them. Boundary values with two additional meshes are transferred with each other using MPI in different configurations. Moving wave front are visualized by applying the MPI in the standard MIMD treatment. The efficiency against the space complexity will be discussed by changing mesh size and number of nodes., 資料番号: AA0000294003, レポート番号: NAL SP-30

航空宇宙技術研究所 7-9 Jun. 1995 東京 日本, National Aerospace Laboratory 7-9 Jun. 1995 Tokyo Japan, ラム/スクラムジェット燃焼器における超音速混合流れ場の数値解析と試験研究を行った。ランプ型インジェクタによる並行噴射を選択し、ランプ生成の超音速混合層における斜め衝撃波の衝突効果を調べた。数値シュリーレン画像の衝撃波パターンと風洞試験のシュリーレン写真は良い一致を示し、壁面静圧分布および空間ピトー全圧分布でも良く一致した。さらに数値解析ではペア縦渦の生成過程や、この渦によるジェットの巻き込みなどの流れ構造を鮮明にとらえることができ、これに基づく検討の結果、斜め衝撃波は噴射気体を壁面から引き上げ、縦渦の渦度を増加することも分かった。以上により、超音速流中への並行噴射における燃料-空気の混合流の数値解析に対して、本研究に用いたCFDコードの有効性が確認できた。ランプ型インジェクタによる縦渦の生成および混合流れ場における斜め衝撃波の効果は、ラム/スクラムジェット燃焼器の燃料-空気混合におけるキーファクタであることが分かった。, Numerical and experimental study were conducted to investigate the structure of supersonic mixing flow field in ram/scramjet combustor. One type of parallel injection method with ramp injector was selected and the effects of oblique shock impingement on supersonic mixing layer generated from the ramp had been studied. The patterns of shock waves in the numerical schlieren image agreed with experimental results in schlieren photograph. Comparisons of static pressure on the wall surface and spatial Pitot pressure distributions showed good agreement qualitatively. Numerical results captured the structures of flow field clearly, which were generating process of a pair of streamwise vortices and vortical roll-up of the jet. The oblique shocks had some effects on the flow field, which made injectant gas lift off from wall surface and increased intensity of streamwise vortices. According to these results, it could be said that the CFD (Computational Fluid Dynamics) code used in this study was useful for investigation of fuel-air mixing in supersonic flow field with parallel injection. From the numerical results mentioned above, it was confirmed that the streamwise vortices generated by ramp injector and interaction between mixing field and oblique shocks were key factors for enhancement of fuel-air mixing in ram/scramjet combustor., 資料番号: AA0000294015, レポート番号: NAL SP-30

本論文の目的は、ラム/スクラムジェット燃焼器の中の超音速混合流れ場の構造を調べ、燃焼器の設計に用いられるべきCFDコードを開発することにある。ランプ型インジェクタからの平行噴射の一形式について数値的および実験的に調べた。数値シミュレーションにより得られた衝撃波パターンは、シュリーレン写眞における実験結果と一致する。壁面静圧分布の比較は定性的に良い一致を示した。数値結果は、主流方向の一対の渦の生成過程や渦に似たジェットの巻き上りなどの流れ場の構造を明かに捉えている。計算や実験で見出されたように、斜め衝撃波は噴射されたガスを壁面から持ち上げる。これらの結果によれば、用いられたCFDコードは、超音速流れの中で平行噴射された燃料と空気の混合の研究に有用である。計算結果から、ランプ型インジェクタにより作られる主流方向の渦や混合流と斜め衝撃波の間の干渉が、ラム/スクラムジェット燃焼器の中の燃料と空気の混合の促進の鍵であることが確かめられた。, The purposes of present paper are to investigate the structure of supersonic mixing flow field in ram/scramjet combustor and to develop the Computational Fluid Dynamics (CFD) code which will be used for the design of the combustor. One type of parallel injection method with ramp injector had been studied numerically and experimentally. The patterns of shock waves obtained by numerical simulations agreed with experimental results in schlieren photograph. Comparisons of static pressure distributions on the wall surface showed good agreement qualitatively. Numerical results captured the structures of flow field clearly, which were generating process of a pair of streamwise vortices and vertical roll-up of the jet. Oblique shocks made injectant gas lift off from wall surface, as found in calculations and experiments. According to these results, it could be said that the CFD code used in this study was useful for investigation of fuel-air mixing in supersonic flow field with parallel injection. From the numerical results, it was confirmed that the streamwise vortices generated by ramp injector and interaction between mixing field and oblique shocks were key factors for enhancement of fuel-air mixing in ram/scramjet combustor., 資料番号: AA0004174007, レポート番号: NAL SP-27

航空宇宙技術研究所 10-11 Jun. 1993 東京 日本, National Aerospace Laboratory 10-11 Jun. 1993 Tokyo Japan, 直角方向の噴射がある超音速混合流れ場の基本的特性を数値的および実験的に調べた。平板上の単一孔から超音速流れ(M=4)に直角に音速ジェットを吹き出す。ピトー圧分布を3次元的に測定した。流れ場の数値シミュレーションを行い実験データと比較した。本研究が定量的に裏付けられ、良好な信頼性をもつことがわかった。数値的および実験的な結果に基づいて本研究における流れ場の現象を論じた。互に反対向きの回転をもつ渦対が平板の近傍で生成され、この渦による巻き込みの結果として混合が生ずる。ジェットの中心はピトー圧の分布から推定した。, A fundamental characteristic of supersonic mixing field with transverse injection is examined by numerical and experimental studies. A sonic jet is injected perpendicularly into supersonic flow (Mach number = four) from a single hole on flat plate. The pitot pressure distribution is measured three dimensionally. Numerical simulation is conducted in the flow field, and is compared with experimental data. It is shown that the present investigation is verified quantitatively and has a good reliability. On the basis of numerical and experimental results, phenomena of the present flow field are discussed. It is observed that the counter rotating vortex pair which rolls up from near the flat plate is generated and the mixing occurs as a result of entraining by these vortexes. Jet core location is estimated from pitot pressure distribution., 資料番号: AA0004171033, レポート番号: NAL SP-22

航空宇宙技術研究所 10-11 Jun. 1993 東京 日本, National Aerospace Laboratory 10-11 Jun. 1993 Tokyo Japan, 航空宇宙技術研究所(NAL)と富士通は共同して、航空宇宙技術分野における数値流体力学のため「数値風洞(NWT)」と呼ばれる並列ベクトル計算機を開発した。NWTはクロスバーネットワークで結ばれた140の要素計算機(PE)から構成される。その全体性能は236ギガフロップス(GFLOPS)で、総記憶容量は35ギガバイトである。3次元CFD(計算空気力学)プログラムを用いた評価では140PEで116GFLOPSを示し、2〜64PEでは最高性能の90％、128PEでは80％、を維持する。, National Aerospace Laboratory and Fujitsu Limited have jointly developed a parallel vector computer called Numerical Wind Tunnel (NWT) for the advancement of Computational Fluid Dynamics (CFD) in the field of aeronautics and space technology. The NWT is composed of 140 Processing Elements (PE) connected with a crossbar network. Its total performance is 236 GigaFLOPS and aggregate memory capacity is 35 GigaBytes. Evaluation results with a three dimensional CFD program show the performance of 116 GigaFLOPS on 140 PEs, and sustain the performance about 90 percent from 2 to 64 PEs, moreover 80 percent on 128 PEs., 資料番号: AA0004171031, レポート番号: NAL SP-22

航空宇宙技術研究所 10-12 Jun. 1992 東京 日本, National Aerospace Laboratory 10-12 Jun. 1992 Tokyo Japan, 数値風洞は、航空宇宙技術研究所(NAL)と富士通(株)との共同により研究開発中のもので、ベクトルプロセッサから成る分散メモリ構成の並列計算機システムである。本論文では、現用の並列言語処理により並列化された2つの応用プログラムについて行ったその性能の机上評価を示す。性能は、ネットワークシミュレータおよびVP400の性能解析に基いた評価ソフトウェアVTAPを用いて評価した。数値風洞は富士通VP400に比べて約100倍速いCFD(計算流体力学)シミュレーション性能をもつという結果を得た。, The Numerical Wind Tunnel (NWT) is under research and development by NAL-Fujitsu joint activity. It is a parallel computer system of distributed memory architecture composed of vector processors. In this paper, the performance on the desk of two application programs that were parallelized by current parallel language processor is shown. The performance using network simulator and evaluation software 'VTAP' which is based on VP400 performance analysis is evaluated. The estimations that the present machine performs CFD (Computational Fluid Dynamics) simulation about 100 times faster than Fujitsu VP400 is presented., 資料番号: AA0004168046, レポート番号: NAL SP-19

航空宇宙技術研究所 10-12 Jun. 1992 東京 日本, National Aerospace Laboratory 10-12 Jun. 1992 Tokyo Japan, 数値風洞(NWT)は、航空宇宙技術研究所(NAL)と富士通(株)との共同により研究開発中のもので、ベクトルプロセッサから成る分散メモリ構成の並列計算機システムである。本論文では、NWT向けの通常のフォートランプログラムに並列化や調整によって段階的に高速実行のための記述をとり入れていく並列フォートランのプログラム法を示す。具体的手順を用いながらその結果を述べた。, The Numerical Wind Tunnel (NWT) is under research and development by NAL-Fujitsu joint activity. It is a parallel computer system of distributed memory architecture composed of vector processors. In this paper, the programming method of parallel Fortran by gradually catching the descriptions for high-speed execution, in the case of parallelizing and tuning usual Fortran programs for NWT is shown. The examination results using a concrete procedure are presented., 資料番号: AA0004168045, レポート番号: NAL SP-19

航空宇宙技術研究所 10-12 Jun. 1992 東京 日本, National Aerospace Laboratory 10-12 Jun. 1992 Tokyo Japan, 高負荷単段軸流圧縮機ロータブレードまわりの遷音速流れ場を、Chakravathy-Osher型TVD(全変動減少型)スキームを用いた3次元ナビエ・ストークス方程式コードにより数値的に調べた。IGV(入口案内翼)およびロータブレードのまわりの流れを同時に計算する段間解析を実施した。設計値および実験データと比較すると、計算は量的にやや異なった結果を与える。しかしながら、数値計算結果は圧縮機の圧力上昇特性および強い衝撃波を含む流れのパターンをよくシミュレートする。, A transonic flowfield around rotor blades of a highly loaded single stage axial compressor was numerically analyzed by a three-dimensional compressible Navier-Stokes equations code using Chakravarthy and Osher type TVD (Total Variation Diminishing) scheme. A stage analysis which calculates both flowfields around IGV (Inlet Guide Vane) and rotor blades simultaneously was carried out. Comparing with design values and experimental data, computed results gave slight difference quantitatively. But the results of numerical calculation simulated well pressure rise characteristics of compressor and its flow pattern including strong shock surface., 資料番号: AA0004168030, レポート番号: NAL SP-19

The Numerical Wind Tunnel (NWT) is under research and development by NAL-Fujitsu joint activity. it is a parallel computer system of distributed memory architecture composed of vector processors, whose goal is to perform CFD simulation about 100 times faster than FACOM VP400. In this paper we show three fundamental functions global data, parallel execution of DO-loop, and data decomposition and allocation, which the language-processor system has to provide in order to realize parallel execution on the NWT. We choose FORTRAN77 as a basic programming language for NWT and add some compiler directives to make effective use of the NWT. In this paper, we also explain the programming model of the NWT and the execution image with these directives., 資料番号: NALSP0016018, レポート番号: NAL SP-16

This paper describes parallelization of Finite Element Methods (FEM) on the Parallel Simulation Machine Cenju. One of the most time consuming problems in FEM which we decided to investigate is nonlinear dynamic finite element analysis. The main loop of the nonlinear dynamic finite element analysis is the loop based on Newton-Raphson method which is composed of the following two stages, namely: 1. Calculation of the Stiffness Matrix 2. Solution of a set of linear equations. We decided to tackle the above two problems independently. Generation of the Stiffness Matrix consists of: Process 1 Per Element Calculation in which the element stiffness matrix as well as the reactance force is calculated for each element. Process 2 Accumulative Calculation in which the element stiffness matrices are combined to form the global stiffness matrix. It is quite straightforward to parallelize Process 1, just allocate a group of elements to processors and let them calculate the values for the elements. On the other hand, Process 2 is not so easy to parallelize. We tried two strategies to parallelize Process 2. By eliminating the serial bottleneck, we were able to attain a speed-up of 48 on a 64 processor system. For parallelizing solution of linear equations, we tried two approaches. 1. Prallelizing LU-Factorization. 2. Parallelizing Conjugate Gradient Methods. We first evaluated parallelizing LU-Factorization on a comparatively small set of data. However, due to insufficient amount of parallelism, the speed-up was low-2.9 using 7 processors. So, we decided to tackle parallelizing the conjugate gradient method. The conjugate gradient method we chose is Scaled Conjugate Gradient Method (SCG) which was developed by Hayami for vector computers. For a large scale matrix (8,904 by 8,904) we were able to attain a speed-up of 36 on a 64 processor system., 資料番号: NALSP0016014, レポート番号: NAL SP-16

Three-dimensional Reynolds-averaged full Navier-Stokes equation including chemical reactions solver is developed to predict flow fields in SCRAMjet engine combustors. Using the above code, sonic gas transverse injections behind the rearward-facing step into the M=3.7 supersonic flow are investigated numerically. The numerical results are compared with the result of the transverse injection on the flat plate. The comparison shows that mixing of injectant gas with main air flow is enhanced by the rearwardfacing step., 資料番号: NALSP0016043, レポート番号: NAL SP-16

The unsteady flowfield with large separation in highly loaded transonic compressor cascade is numerically analyzed by the implicit time marching method solving two-dimensional Navier-Stokes cquations. It is effective for the aerodynamic design of improved compressor cascade to make possible accurate prediction of the aerodynamic performances such as total pressure loss or exit flow angle, even with large boundary layer separation. In this study, several computational trials including the unsteady simulation without using thin layer approximation nor any turbulence models are investigated., 資料番号: NALSP0014035, レポート番号: NAL SP-14

The steady inviscid compressible flow through a three-dimensional cascade is computed by Denton's original Time-Dependent Finite Volume Method. We are developing a research code, working code, and production code in order to analyze three-dimensional cascade flows. The present paper is concerned with the numerical results obtained during the course of development, adopting the RD-blade(2) for a test case. Two types of evaluation of flux vector through up and down stream surface of the integral domain are compared. In the steady state, the computed Mach number shows good agreement with the experimental isentropic one, except near both leading and trailing edges on the suction surface, although computed isentropic Mach numbers differ somewhat from those obtained in experiments on the fore part of the compression surface. This is caused by computed total pressure variation resulting from low static pressure on the compression surface. In the case of our two-dimensional computations based on McDonald's Finite Area Method, such difference resulted from somewhat inaccurate density. This problem has almost been overcome by the research of Nishimura et. al.15) In the three-dimensional case, it is expected that his approach is also applicable to overcome present difficulties., 資料番号: NALSP0001008, レポート番号: NAL SP-1

資料番号: NALSP0010027, レポート番号: NAL SP-10

The Numerical Simulator System installed at NAL Computational Sciences Division in Feb. 1987 is working well for computational research activities. This report describes the background and the course of the system installation, the illustration of the system configuration and utilization, and the examples of advanced computational results. The factors affecting the progress of Research Computational Fluid Dynamics, primarily supercomputer hardware, are mentioned., 資料番号: NALSP0008001, レポート番号: NAL SP-8

In recent years, numerical simulation method based on viscous equation is widely applied to aerodynamic research and development in the field of airfoil, wing, fuselage, etc. It is proved powerful, and the application of this method to propellar blades research and development, especially for the ATP-blades, is natural. While many experiences with two-dimensional viscous simulation for thick airfoils are accumulated, however experience for such thin airfoils with very sharp leading edge as often propeller blades have the characteristics is relatively few. The verification of the two-dimensional viscous simulation codes, NSFOIL and NS2D applied to one of those airfoils, NACA 16-204 airfoil which was tested by the two-dimensional wind tunnel at NAL last year, is main object of the present report. Mach number sweeps at low angles of attack and angle of attack sweeps at M=0.6 and 0.85 were made. The comparison of the computed aerodynamic characteristics with the wind tunnel data assure us that the method is useful in this field, although some improvements of the codes are to be desired., 資料番号: NALSP0009034, レポート番号: NAL SP-9

当所に大型計算機が導入されてから十数年になるが,科学技術計算用の標準的なサブルーチンというものがない。そこで,これらのものの作成にとりかかることにした。まず第一に,線型計算関係を取り扱うことにし,今回はその中でも,係数行列が正定値である場合の,方程式系の解法及び逆行列の計算に関するサブルーチンについて報告する。解法としては,本質的には2つの方法-コレスキー分解法とガウス・ジョルダン法-を採用した。, 資料番号: NALTM0277000, レポート番号: NAL TM-277

本報告は,一連の一次方程式系を取り扱ったもののうち,長方行列を対象としたものである。そのうち主として最小自乗問題の解法を取り扱い,特殊な場合のものとして,実正方行列の逆行列を計算するものがある。方法としては,ハウスホルダー変換を利用したもの,消去法型の直交化法を利用したもの,及びsingular value decompositionを利用したものの3つがある。, 資料番号: NALTM0315000, レポート番号: NAL TM-315

The steady inviscid compressible flow through the two-dimensional cascade is computed by the Method of Time-Dependent Finite Area with hexagonal integral domain. Three different equation systems are considered which are physically equivalent under two assumptions: i) steady state, ii)subsonic or exsting weak shock flow field. The basic system is composed of the continuity equation, the Eular equation and the energy equation. Their differences during numerical behavior approaching the steady state have been examined through computations. To prevent the pressure or the density from becoming negative, the spatial averaging for smoothing was used, which appears to have some artificial viscocity and damping factor for time-dependent computations. In the steady state computed airfoil pressure distributions have shown good agreement with experimental measurements and there have been few differences among the three equation systems., 資料番号: NALTR0709000, レポート番号: NAL TR-709

当計算センタにFACOM 230-75APが導入されてからすでに一年以上経過した。その理論的評価及び単体命令の実測評価については文献〔1〕に,その他の実測評価及びコーディング技法に関する注意については文献〔2〕にそれぞれ発表されている。ここではこれまでにすでに発表した3),4),5)線型計算関係のCP用サブルーチンをAP用に変換したものの性能-精度,速度-を調べた結果を報告する。, More than a year has passed since the FACOM 230-75 Array Processor System was installed in the Computer center, National Aerospace Laboratory. Its theoretical assessment and the actual speed of operations has already been reported. 1) The other results from the measurements and some comments on the coding techniques were given in another report. 2) The AP-subroutines solving linear equation systems were translated from the CP-subroutines based on the ‘Handbook for Automatic Computation’edited by J.H.Wilkinson and C.Reinisch, on which we have already reported. The present paper is concerned with the results, the speed and the accuracy, and running them on the FACOM 230-75 Array Processor., 資料番号: NALTR0579000, レポート番号: NAL TR-579

本報告は,最も基本的と思われる1次方程式系 Ax=b を,Aが実又は複素稠密行列であるとき及び実帯状行列であるときの2通りの場合に分けて取り扱ったものである。解法としては直接法であるLU-分解法を使用した。さらに,多くのテスト結果によってこのような簡単な問題を解くのにも種々の問題点があることを,特にライブラリー使用者に向けて指摘した。なお,実帯状行列の場合についてのみinverse iteration法による固有ベクトルの計算法をも掲載した。(ここで作成したLU-分解法のサブルーチンを使用しているためである), 資料番号: NALTM0348000, レポート番号: NAL TM-348