4 参考文献
参考文献
[1] Hirsch C. Numerical computation of internal and external flows, vols. 1 and 2. Chichester, UK: John Wiley and Sons; 1988.
题名中译：内流与外流的数值计算（第 1、2 卷）。
[2] Mohanraj R, Neumeier Y, Zinn BT. Characteristic-based treatment of source terms in Euler equations for Roe scheme. AIAA J 1999;37:417-24.
题名中译：Roe 格式中 Euler 方程源项的特征处理。
[3] Jameson A, Baker TJ. Solution of the Euler equations for complex configurations. AIAA Paper 83-1929; 1983.
题名中译：复杂构型 Euler 方程的求解。
[4] Rossow C-C. Berechnung von Strömungsfeldern durch Lösung der Euler-Gleichungen mit einer erweiterten Finite-Volumen Diskretisierungsmethode [Calculation of flow fields by the solution of Euler equations using an extended finite volume discretization scheme]. DLR Research Report No. 89-38; 1989.
题名中译：采用扩展有限体积离散方法求解 Euler 方程以计算流场。
[5] Bruner, CWS. Geometric properties of arbitrary polyhedra in terms of face geometry. AIAA J 1995;33:1350.
题名中译：用面几何描述任意多面体的几何性质。
[6] www.ma.ic.ac.uk/~rn/centroid.pdf
资源说明：网络资源（原文仅给出链接，未列题名）。
[7] Jameson A, Schmidt W, Turkel E. Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time-stepping schemes. AIAA Paper 81-1259; 1981.
题名中译：采用 Runge–Kutta 时间推进格式的有限体积法求解 Euler 方程。
[8] Ni RH. Multiple grid scheme for solving the Euler equations. AIAA Paper 81-1025; 1981.
题名中译：求解 Euler 方程的多网格格式。
[9] Hall MG. Cell-vertex multigrid scheme for solution of the Euler equations. In: Proc. int. conf. on numerical methods for fluid dynamics. Reading, UK: Springer Verlag; 1985.
题名中译：求解 Euler 方程的单元顶点多重网格格式。
[10] Radespiel R. A cell-vertex multigrid method for the Navier-Stokes equations. NASA TM-101557; 1989.
[11] Radespiel R, Rossow C-C, Swanson RC. An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations. AIAA Paper 89-1953; 1989 [also in AIAA J 1990;28:1464-72].
[12] Rossow C-C. Flux balance splitting—a new approach for a cell-vertex upwind scheme. In: Proc. 12th int. conf. on numerical methods in fluid dynamics. Oxford, UK: Springer Verlag; 1990.
题名中译：通量平衡分裂——单元顶点迎风格式的一种新方法。
[13] Rossow C-C. Accurate solution of the 2D Euler equations with an efficient cell-vertex upwind scheme. AIAA Paper 93-0071; 1993.
题名中译：采用高效单元顶点迎风格式精确求解二维 Euler 方程。
[14] Usab WJ. Embedded mesh solutions of the Euler equations using a multiple-grid method. Ph.D. Thesis, MIT, Cambridge, MA, USA; 1983.
题名中译：采用多网格方法的 Euler 方程嵌入网格解法。
[15] Sidilkover D. A genuinely multidimensional upwind scheme and efficient multigrid solver for the compressible Euler equations. ICASE Report No. 94-84; 1994.
题名中译：可压缩 Euler 方程的真正多维迎风格式与高效多重网格求解器。
[16] Paillére H, Deconinck H, Roe PL. Conservative upwind residual-distribution schemes based on the steady characteristics of the Euler equations. AIAA Paper 95-1700; 1995.
题名中译：基于 Euler 方程定常特征的守恒迎风残差分配格式。
[17] Issman E, Degrez G, Deconinck H. Implicit upwind residual-distribution Euler and Navier-Stokes solver on unstructured meshes. AIAA J 1996;34:2021-8.
题名中译：非结构网格上的隐式迎风残差分配 Euler 和 Navier–Stokes 求解器。
[18] Van der Weide E, Deconinck H. Compact residual-distribution scheme applied to viscous flow simulations. VKI Lecture Series 1998-03; 1998.
题名中译：用于黏性流模拟的紧致残差分配格式。
[19] Dick E. A flux-difference splitting method for steady Euler equations. J Comput Phys 1988;76:19–32.
题名中译：定常 Euler 方程的通量差分分裂方法。
[20] Hall M. A vertex-centroid scheme for improved finite-volume solution of the Navier-Stokes equations. AIAA Paper 91-1540; 1991.
[21] Crumpton PI, Shaw GJ. A vertex-centred finite volume method with shock detection. Int J Numer Meth Fluids 1994;18:605-25.
题名中译：带激波检测的顶点中心有限体积方法。
[22] Roe PL. Error estimates for cell-vertex solutions of the compressible Euler equation. ICASE Report No. 87-6; 1987.
题名中译：可压缩 Euler 方程单元顶点解的误差估计。
[23] Hoffman JD. Relationship between the truncation errors of centered finite-difference approximations on uniform and nonuniform meshes. J Comput Phys 1982;46:464–74.
题名中译：均匀与非均匀网格上中心有限差分近似截断误差的关系。
[24] Arts T. On the consistency of four different control surfaces used for finite area blade-to-blade calculations. Int J Numer Meth Fluids 1984;4:1083-96.
题名中译：叶片间有限面积计算所用四种不同控制面的相容性。
[25] Turkel E. Accuracy of schemes with non-uniform meshes for compressible fluid flows. ICASE Report No. 85-43; 1985.
题名中译：非均匀网格可压缩流格式的精度。
[26] Turkel E, Yaniv S, Landau U. Accuracy of schemes for the Euler equations with non-uniform meshes. ICASE Report No. 85-59; 1985.
题名中译：非均匀网格 Euler 方程格式的精度。
[27] Rossow C-C. Comparison of cell-centered and cell-vertex finite volume schemes. In: Proc. 7th GAMM conference, notes on numerical fluid mechanics. Wiesbaden: Vieweg Publishing; 1987.
题名中译：单元中心与单元顶点有限体积格式的比较。
[28] Venkatakrishnan V. Implicit schemes and parallel computing in unstructured grid CFD. ICASE Report No. 95-28; 1995.
题名中译：非结构网格 CFD 中的隐式格式与并行计算。
[29] Venkatakrishnan V, Mavriplis DJ. Implicit method for the computation of unsteady flows on unstructured grids. J. Comput Phys 1996;127:380-97.
题名中译：非结构网格非定常流计算的隐式方法。
[30] Van Leer B. Towards the ultimate conservative difference scheme. V. A second order sequel to Godunov's method. J Comput Phys 1979;32:101-36.
题名中译：迈向最终的守恒差分格式。Ⅴ. Godunov 方法的二阶扩展。
[31] Leonard BP. Comparison of truncation error of finite-difference and finite-volume formulations of convection terms. NASA TM-105861; 1992.
题名中译：对流项有限差分与有限体积表述的截断误差比较。
[32] Martinelli L. Calculation of viscous flows with a multigrid method. Ph.D. Thesis, Dept. of Mech. and Aerospace Eng., Princeton University; 1987.
题名中译：采用多重网格方法计算黏性流。
[33] Martinelli L, Jameson A. Validation of a multigrid method for Reynolds averaged equations. AIAA Paper 88-0414; 1988.
题名中译：Reynolds 平均方程多重网格方法的验证。
[34] Yoon S, Kwak D. Artificial dissipation models for hypersonic external flow. AIAA Paper 88-3708; 1988.
题名中译：高超声速外流的人工耗散模型。
[35] Turkel E, Swanson RC, Vatsa VN, White JA. Multigrid for hypersonic viscous two- and three-dimensional flows. AIAA Paper 91-1572; 1991.
题名中译：高超声速二维与三维黏性流的多重网格方法。
[36] Swanson RC, Turkel E. On central difference and upwind schemes. J Comput Phys 1992;101:292-306.
题名中译：关于中心差分格式与迎风格式。
[37] Jameson A. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flow. AIAA Paper 93-3559; 1993.
题名中译：人工扩散、迎风偏置、限制器及其对跨声速和高超声速流精度与多重网格收敛的影响。
[38] Swanson RC, Radespiel R, Turkel E. Comparison of several dissipation algorithms for central difference schemes. ICASE Report No. 97-40; 1997 [also AIAA Paper 97-1945, 1997].
题名中译：中心差分格式的多种耗散算法比较。
[39] Pulliam TH. Artificial dissipation models for the Euler equations. AIAA J 1986;24:1931-40.
题名中译：Euler 方程的人工耗散模型。
[40] Van Leer B. Flux-vector splitting for the Euler equations. In: Proc. 8th Int. conf. on numerical methods in fluid dynamics, Springer Verlag; 1982. p. 507-12 [also ICASE Report 82-30; 1982].
题名中译：Euler 方程的通量矢量分裂。
[41] Liou M-S, Steffen Jr CJ. A new flux splitting scheme. NASA TM-104404, 1991; also J Comput Phys 1993;107:23-39.
题名中译：一种新的通量分裂格式。
[42] Liou M-S. A sequel to AUSM: AUSM+. J Comput Phys 1996;129:364-82.
题名中译：AUSM 的后续发展：AUSM+。
[43] Jameson A. Artificial diffusion, upwind biasing, limiters and their effect on accuracy and multigrid convergence in transonic and hypersonic flow. AIAA Paper 93-3559; 1993.
题名中译：人工扩散、迎风偏置、限制器及其对跨声速和高超声速流精度与多重网格收敛的影响。
[44] Tatsumi S, Martinelli L, Jameson A. A new high resolution scheme for compressible viscous flow with shocks. AIAA Paper 95-0466; 1995.
题名中译：含激波可压缩黏性流的一种新高分辨率格式。
[45] Edwards JR. A low-diffusion flux-splitting scheme for Navier-Stokes calculations. Comput Fluids 1997;26:653-9.
[46] Rossow C-C. A simple flux splitting scheme for compressible flows. In: Proc. 11th DGLR-Fach-symposium, Berlin, Germany; November 10-12, 1998.
题名中译：可压缩流的一种简单通量分裂格式。
[47] Rossow C-C. A flux splitting scheme for compressible and incompressible flows. AIAA Paper 99-3346; 1999.
题名中译：可压缩与不可压缩流的通量分裂格式。
[48] Thomas JL, van Leer B, Walters RW. Implicit flux-split schemes for the Euler equations. AIAA Paper 85-1680; 1985.
题名中译：Euler 方程的隐式通量分裂格式。
[49] Anderson WK, Thomas JL, van Leer B. A comparison of finite volume flux vector splittings for the Euler equations. AIAA J 1986;24:1453-60.
题名中译：Euler 方程有限体积通量矢量分裂的比较。
[50] Hänel D, Schwane R, Seider G. On the accuracy of upwind schemes for the solution of the Navier-Stokes equations. AIAA Paper 87-1105; 1987.
[51] Van Leer B, Thomas JL, Roe PL, Newsome RW. A comparison of numerical flux formulas for the Euler and Navier-Stokes equations. AIAA Paper 87-1104; 1987.
[52] Hänel D, Schwane R. An implicit flux-vector scheme for the computation of viscous hypersonic flows. AIAA Paper 89-0274; 1989.
题名中译：计算黏性高超声速流的隐式通量矢量格式。
[53] Van Leer B. Flux vector splitting for the 1990's. In: Invited Lecture for the CFD Symposium on Aeropropulsion, Cleveland, OH; 1990.
题名中译：面向 20 世纪 90 年代的通量矢量分裂。
[54] Seider G, Hänel D. Numerical influence of upwind TVD schemes on transonic airfoil drag prediction. AIAA Paper 91-0184; 1991.
题名中译：迎风 TVD 格式对跨声速翼型阻力预测的数值影响。
[55] Liou MS. On a new class of flux splittings. In: Proc. 13th int. conf. on numerical methods in fluid dynamics, Rome, Italy; 1992.
题名中译：一类新的通量分裂方法。
[56] Wada Y, Liou M-S. A flux splitting scheme with high-resolution and robustness for discontinuities. AIAA Paper 94-0083; 1994.
题名中译：对间断具有高分辨率和稳健性的通量分裂格式。
[57] Liou M-S. Progress towards an improved CFD method – AUSM+. AIAA Paper 95-1701; 1995.
题名中译：迈向改进 CFD 方法的进展——AUSM+。
[58] Radespiel R, Kroll N. Accurate flux vector splitting for shocks and shear layers. J Comput Phys 1995;121:66-78.
题名中译：激波与剪切层的高精度通量矢量分裂。
[59] Edwards JR. Numerical implementation of a modified Liou-Steffen upwind scheme. AIAA J 1994;32:2120-22.
题名中译：改进 Liou–Steffen 迎风格式的数值实现。
[60] Jameson A. Positive schemes and shock modelling for compressible flow. Int J Numer Meth Fluids 1995;20:743-76.
题名中译：可压缩流的保正格式与激波建模。
[61] Jameson A. Analysis and design of numerical schemes for gas dynamics. II: Artificial diffusion and discrete shock structure. Int J Comput Fluid Dynam 1995;5:1-38.
题名中译：气体动力学数值格式的分析与设计。Ⅱ：人工扩散与离散激波结构。
[62] Tatsumi S, Martinelli L, Jameson A. A design, implementation and validation of flux limited schemes for the solution of the compressible Navier-Stokes equations. AIAA Paper 94-0647; 1994.
[63] Nemec M, Zingg DW. Aerodynamic computations using the convective upstream split pressure scheme with local preconditioning. AIAA Paper 98-2444; 1998.
题名中译：采用局部预处理的对流迎风分裂压力格式进行空气动力学计算。
[64] Roe PL. Approximate Riemann solvers, parameter vectors, and difference schemes. J Comput Phys 1981;43:357-72.
题名中译：近似 Riemann 求解器、参数矢量与差分格式。
[65] Godunov SK. A difference scheme for numerical computation discontinuous solution of hydrodynamic equations. Math Sbornik [in Russian] 1959;47:271-306 [translated US Joint Publ. Res. Service, JPRS 7226, 1969].
题名中译：数值计算流体动力学方程间断解的一种差分格式（原文为俄文，另有英译本）。
[66] Osher S, Solomon F. Upwind difference schemes for hyperbolic systems of conservation laws. Math Comput 1982;38:339-74.
题名中译：双曲型守恒律方程组的迎风差分格式。
[67] Roe PL, Pike J. Efficient construction and utilisation of approximate Riemann solutions. In: Glowinski R, Lions JL, editors. Computing methods in applied sciences and engineering. The Netherlands: North Holland Publishing; 1984.
题名中译：近似 Riemann 解的高效构造与使用；收录于《应用科学与工程中的计算方法》。
[68] Peery KM, Imlay ST. Blunt-body flow simulations. AIAA Paper 88-2904; 1988.
题名中译：钝体流动模拟。
[69] Lin HC. Dissipation additions to flux-difference splitting. AIAA Paper 91-1544; 1991.
题名中译：通量差分分裂的附加耗散。
[70] Quirk JJ. A contribution to the great Riemann solver debate. ICASE Report No. 92-64; 1992.
题名中译：关于 Riemann 求解器大讨论的一项研究。
[71] Harten A, Lax PD, Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. Soc Indust Appl Math Rev 1983;25(1):35-61.
题名中译：双曲型守恒律的上游差分与 Godunov 型格式。
[72] Harten A, Hyman JM. Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J Comput Phys 1983;50:235-69.
题名中译：一维双曲型守恒律的自调节网格方法。
[73] Vinokur M. Flux Jacobian matrices and generalized Roe average for an equilibrium real gas. NASA CR-177512; 1988.
题名中译：平衡真实气体的通量 Jacobian 矩阵与广义 Roe 平均。
[74] Vinokur M, Montagné J-L. Generalized flux-vector splitting and Roe average for an equilibrium real gas. J Comput Phys 1990;89:276-300.
题名中译：平衡真实气体的广义通量矢量分裂与 Roe 平均。
[75] Grossman B, Cinnella P. Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation. J Comput Phys 1990;88:131-68.
题名中译：具有非平衡化学与振动松弛的流动通量分裂算法。
[76] Shuen J-S, Liou M-S, Van Leer B. Inviscid flux-splitting algorithms for real gases with non-equilibrium chemistry. J Comput Phys 1990;90:371-95.
题名中译：具有非平衡化学的真实气体无黏通量分裂算法。
[77] Mulas M, Chibbaro S, Delussu G, Di Piazza I, Talice M. Efficient parallel computations of flows of arbitrary fluids for all regimes of Reynolds, Mach and Grashof Numbers. Int J Numer Meth Heat Fluid Flow 2002;12:637-57.
题名中译：任意流体在全部 Reynolds 数、Mach 数和 Grashof 数范围内流动的高效并行计算。
[78] Harten A. High resolution schemes for hyperbolic conservation laws. J Comput Phys 1983;49:357-93.
题名中译：双曲型守恒律的高分辨率格式。
[79] Jameson A, Lax PD. Conditions for the construction of multi-point total variation diminishing difference schemes. MAE Report 1650, Dept. of Mechanical and Aerospace Engineering, Princeton University; 1984.
题名中译：构造多点总变差减小差分格式的条件。
[80] Davis SF. TVD finite difference schemes and artificial viscosity. ICASE Report No. 84–20; 1984.
题名中译：TVD 有限差分格式与人工黏性。
[81] Yee HC. Construction of implicit and explicit symmetric TVD schemes and their applications. J Comput Phys 1987;68:151-79.
题名中译：隐式与显式对称 TVD 格式的构造及其应用。
[82] Yee HC, Kutler P. Application of second-order accurate total variation diminishing (TVD) schemes to the Euler equations in general geometries. NASA TM-85845; 1983.
题名中译：二阶精度总变差减小（TVD）格式在一般几何 Euler 方程中的应用。
[83] Yee HC. Upwind and symmetric shock-capturing schemes. NASA TM-89464; 1987.
题名中译：迎风与对称激波捕捉格式。
[84] Yee HC, Harten A. Implicit TVD schemes for hyperbolic conservation laws in curvilinear coordinates. AIAA J 1987;25:266-74.
题名中译：曲线坐标系中双曲型守恒律的隐式 TVD 格式。
[85] Yee HC, Klopfer GH, Montagné J-L. High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows. NASA TM-100097; 1988.
题名中译：无黏与黏性高超声速流的高分辨率激波捕捉格式。
[86] Yee HC. A class of high-resolution explicit and implicit shock-capturing methods. VKI Lecture Series 1989-04; 1989 [also NASA TM-101088; 1989].
题名中译：一类高分辨率显式与隐式激波捕捉方法。
[87] Kroll N, Gaitonde D, Aftosmis M. A systematic comparative study of several high resolution schemes for complex problems in high speed flows. In: 29th AIAA Aerospace Sci. Meeting and Exhibit, Reno, USA; 1991.
题名中译：高速流复杂问题中多种高分辨率格式的系统比较研究。
[88] Kroll N, Rossow C-C. A high resolution cell vertex tvd scheme for the solution of the two- and three-dimensional Euler equations. 12th International Conf. on Numerical Methods in Fluid Dynamics, Oxford, UK; 1990.
题名中译：求解二维和三维 Euler 方程的高分辨率单元顶点 TVD 格式。
[89] Müller B. Simple improvements of an upwind TVD scheme for hypersonic flow. AIAA Paper 89-1977; 1989.
题名中译：高超声速流迎风 TVD 格式的简单改进。
[90] Blazek J. Methods to accelerate the solutions of the Euler- and Navier-Stokes equations for steady-state super- and hypersonic flows. Translation of DLR Research Report 94-35, ESA-TT-1331; 1995.
题名中译：加速定常超声速和高超声速流 Euler 与 Navier–Stokes 方程求解的方法（DLR 研究报告英译本）。
[91] LeVeque RJ. Numerical methods for conservation laws. Basel, Switzerland: Birkhäuser Verlag; 1992.
题名中译：守恒律的数值方法。
[92] Spekreijse SP. Multigrid solution of the steady Euler equations. Ph.D. Dissertation, Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands; 1987.
题名中译：定常 Euler 方程的多重网格解法。
[93] Venkatakrishnan V. Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations. AIAA J 1991;29:1092-110.
[94] Van Albada GD, Van Leer B, Roberts WW. A comparative study of computational methods in cosmic gas dynamics. Astron Astrophys 1982;108:76–84.
题名中译：宇宙气体动力学计算方法的比较研究。
[95] Venkatakrishnan V. On the accuracy of limiters and convergence to steady state solutions. AIAA Paper 93-0880; 1993.
题名中译：限制器的精度与向定常解的收敛。
[96] Hemker PW, Koren B. Multigrid, defect correction and upwind schemes for the steady Navier-Stokes equations. In: Synopsis, HERMES Hypersonic Research Program Meeting, Stuttgart, Germany; 1987.
[97] Radespiel R, Swanson RC. An investigation of cell centred and cell vertex multigrid schemes for the Navier-Stokes equations. AIAA Paper 89-0548; 1989.
[98] Radespiel R. A cell-vertex multigrid method for the Navier-Stokes equations. NASA TM-101557; 1989.
[99] Swanson RC, Radespiel R. Cell centered and cell vertex multigrid schemes for the Navier-Stokes equations. AIAA J 1991;29:697-703.
[100] Morton KW, Paisley MF. On the cell-centre and cell-vertex approaches to the steady Euler equations and the use of shock fitting. In: Proc. int. conf. num. meth. fluid dynamics 10, Beijing, China; 1986.
题名中译：定常 Euler 方程的单元中心与单元顶点方法以及激波拟合的应用。
[101] Dimitriadis KP, Leschziner MA. Multilevel convergence acceleration for viscous and turbulent transonic flows computed with cell-vertex method. In: Proc. 4th Copper Mountain conference on multigrid methods. Colorado: SIAM; 1989. p. 130-48.
题名中译：采用单元顶点方法计算的黏性与湍流跨声速流动的多层收敛加速。
[102] Dick E. A flux-vector splitting method for steady Navier-Stokes equations. Int J Numer Meth Fluids 1988;8:317-26.
[103] Dick E. A multigrid method for steady incompressible Navier-Stokes equations based on partial flux splitting. Int J Numer Meth Fluids 1989;9:113-20.
题名中译：基于部分通量分裂的定常不可压缩 Navier–Stokes 方程多重网格方法。
[104] Crumpton PI, Mackenzie JA, Morton KW. Cell vertex algorithms for the compressible Navier-Stokes equations. J Comput Phys 1993;109:1-15.