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Computational Mechanics
Erschienen in: Computational Mechanics 3/2021

20.01.2021 | Original Paper

Stabilized methods for high-speed compressible flows: toward hypersonic simulations

verfasst von: David Codoni, Georgios Moutsanidis, Ming-Chen Hsu, Yuri Bazilevs, Craig Johansen, Artem Korobenko

Erschienen in: Computational Mechanics | Ausgabe 3/2021

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Abstract

A stabilized finite element framework for high-speed compressible flows is presented. The Streamline-Upwind/Petrov–Galerkin formulation augmented with discontinuity-capturing (DC) are the main constituents of the framework that enable accurate, efficient, and stable simulations in this flow regime. Full- and reduced-energy formulations are employed for this class of flow problems and their relative accuracy is assessed. In addition, a recently developed DC formulation is presented and is shown to be particularly well suited for hypersonic flows. Several verification and validation cases, ranging from 1D to 3D flows and supersonic to the hypersonic regimes, show the excellent performance of the proposed framework and set the stage for its deployment on more advanced applications.
Vorheriger Artikel Phase field modeling of ductile fracture at large plastic strains using adaptive isotropic remeshing
Nächster Artikel Adaptive numerical integration of exponential finite elements for a phase field fracture model

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Literatur
1.
Ahrabi BR, Mavriplis DJ (2020) An implicit block ilu smoother for preconditioning of Newton–Krylov solvers with application in high-order stabilized finite-element methods. Comput Methods Appl Mech Eng 358:112637MathSciNetMATH
2.
Aliabadi SK, Tezduyar TE (1993) Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Comput Methods Appl Mech Eng 107(1–2):209–223MATH
3.
Almeida RC, Galeão AC (1996) An adaptive Petrov–Galerkin formulation for the compressible Euler and Navier–Stokes equations. Comput Methods Appl Mech Eng 129(1):157–176MathSciNetMATH
4.
Arisman CJ, Johansen CT, Bathel BF, Danehy PM (2015) Investigation of gas seeding for planar laser-induced fluorescence in hypersonic boundary layer. AIAA J 53(12):3637–3651
5.
Baba K, Tabata M (1981) On a conservative upwind finite element scheme for the convective diffusion equations. RAIRO Analyse Numerique 15(1):3–25MathSciNetMATH
6.
Bazilevs Y, Kamensky D, Moutsanidis G, Shende S (2020) Residual-based shock capturing in solids. Comput Methods Appl Mech Eng 358:112638MathSciNetMATH
7.
8.
Brooks AN, Hughes TJR (1982) Streamline upwind/Petrov–Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations. Comput Methods Appl Mech Eng 32:199–259MathSciNetMATH
9.
Celik IB et al (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. J Fluids Eng 130(7):07
10.
Carter JE (1972) Numerical solutions of the Navier–Stokes equations for the supersonic laminar flow over a two-dimensional compression corner. Technical report, nasa-tr-r-385, NASA Langley Research Center; Hampton, VA, United States
11.
Catabriga L, Coutinho ALGA, Tezduyar TE (2005) Compressible flow SUPG parameters computed from element matrices. Commun Numer Methods Eng 21:465–476MathSciNetMATH
12.
Catabriga L, Coutinho ALGA, Tezduyar TE (2006) Compressible flow SUPG stabilization parameters computed from degree-of-freedom submatrices. Comput Mech 38:334–343MATH
13.
Chalot F, Hughes TJR (1994) A consistent equilibrium chemistry algorithm for hypersonic flows. Comput Methods Appl Mech Eng 112:25–40MATH
14.
Chalot F, Hughes TJR, Shakib F (1990) Symmetrization of conservation laws with entropy for high-temperature hypersonic computations. Comput Syst Eng 1(2–4):495–521
15.
Chapman S, Cowling TG (1970) The mathematical theory of nonuniform gases. Cambridge University Press, CambridgeMATH
16.
Danehy P, Bathel B, Ivey C, Inman J, Jones S (2009) NO PLIF study of hypersonic transition over a discrete hemispherical roughness element. In: 47th AIAA aerospace sciences meeting including the new horizons forum and aerospace exposition
17.
Denman ED, Beavers AN (1976) The matrix sign function and computations in systems. Appl Math Comput 2(1):63–94MathSciNetMATH
18.
Dick E (2009) Introduction to finite element methods in computational fluid dynamics. In: Wendt JF (ed) Computational fluid dynamics, chapter 10. Springer, Berlin
19.
Dumbser M, Moschetta JM, Gressier J (2003) A matrix stability analysis of the carbuncle phenomenon. J Comput Phys 197:647–670MATH
20.
Edquist KT (2006) Computations of Viking Lander capsule hypersonic aerodynamics with comparisons to ground and flight data. In: AIAA atmospheric flight mechanics conference and exhibit
21.
Elling V (2009) The carbuncle phenomenon is incurable. Acta Mathematica Scientia 29(6):1647–1656MathSciNetMATH
22.
Flaherty T (1972) Aerodynamics data book, ver-10. TR-3709014, Martin Marietta Corporation, Denver Division
23.
Hauke G (2001) Simple stabilizing matrices for the computation of compressible flows in primitive variables. Comput Methods Appl Mech Eng 190:6881–6893MATH
24.
Hauke G, Hughes TJR (1994) A unified approach to compressible and incompressible flows. Comput Methods Appl Mech Eng 113:389–395MathSciNetMATH
25.
Hauke G, Hughes TJR (1998) A comparative study of different sets of variables for solving compressible and incompressible flows. Comput Methods Appl Mech Eng 153:1–44MathSciNetMATH
26.
Hirschfelder JO, Curtiss CF, Bird RB (1954) Molecular theory of gases and liquids. Wiley, HobokenMATH
27.
Hollis BR (1996) Real-gas flow properties for NASA Langley research center aerothermodynamic facilities complex wind tunnels. Nasa contractor report 4755, NASA Langley Research Center; Hampton, VA, United States
28.
Hughes TJR, Franca LP, Hulbert GM (1989) A new finite element formulation for computational fluid dynamics: VIII the Galerkin/least-squares method for advective-diffusive equations. Comput Methods Appl Mech Eng 73:173–189MathSciNetMATH
29.
Hughes TJR, Franca LP, Mallet M (1986) A new finite element formulation for computational fluid dynamics: I symmetric forms of the compressible Euler and Navier–Stokes equations and the second law of thermodynamics. Comput Methods Appl Mech Eng 54:223–234MathSciNetMATH
30.
Hughes TJR, Franca LP, Mallet M (1987) A new finite element formulation for computational fluid dynamics: VI convergence anaysis of the generalized SUPG formulation for linear time-dependent multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 63:97–112MATH
31.
Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: III the generalized streamline operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58:305–328MathSciNetMATH
32.
Hughes TJR, Mallet M (1986) A new finite element formulation for computational fluid dynamics: IV a discontinuity-capturing operator for multidimensional advective–diffusive systems. Comput Methods Appl Mech Eng 58:329–336MathSciNetMATH
33.
Hughes TJR, Mallet M, Mizukami A (1986) A new finite element formulation for computational fluid dynamics: II beyond SUPG. Comput Methods Appl Mech Eng 54:341–355MathSciNetMATH
34.
Hughes TJR, Tezduyar TE (1984) Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. Comput Methods Appl Mech Eng 45:217–284MathSciNetMATH
35.
Ingoldby RN, Michel FC, Flaherty TM, Doryand MG, Preston B, Villyard KW, Steele RD (1976) Entry data analysis for viking landers 1 and 2 final report. NASA CR-159388, Martin Marietta Corporation, Denver Division
36.
Jansen KE, Whiting CH, Hulbert GM (2000) A generalized-\(\alpha \) method for integrating the filtered Navier–Stokes equations with a stabilized finite element method. Comput Methods Appl Mech Eng 190:305–319MathSciNetMATH
37.
Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, CambridgeMATH
38.
Johnson C, Navert U, Pitkaranta J (1984) Finite element methods for linear hyperbolic problems. Comput Methods Appl Mech Eng 45:285–312MathSciNetMATH
39.
Johnson C, Szepessy A (1987) On the convergence of a finite element method for a nonlinear hyperbolic conservation law. Math Comput 49(180):427–444MathSciNetMATH
40.
Johnson C, Szepessy A, Hansbo P (1990) On the convergence of shock-capturing streamline diffusion finite element methods for hyperbolic conservation laws. Math Comput 54(189):107–129MathSciNetMATH
41.
Kanai T, Takizawa K, Tezduyar TE, Tanaka T, Hartmann A (2019) Compressible-flow geometric-porosity modeling and spacecraft parachute computation with isogeometric discretization. Comput Mech 63:301–321MathSciNetMATH
42.
Kirk BS, Stogner RH, Bauman PT, Oliver TA (2014) Modeling hypersonic entry with the fully-implicit Navier–Stokes (fin-s) stabilized finite element flow solver. Comput Fluids 92:281–292MathSciNetMATH
43.
Kozak N, Rajanna MR, Wu MCH, Murugan M, Bravo L, Ghoshal A, Hsu MC, Bazilevs Y (2020) Optimizing gas turbine performance using the surrogate management framework and high-fidelity flow modeling. Energies 13(17):4283
44.
Kuraishi T, Takizawa K, Tezduyar TE (2019) Tire aerodynamics with actual tire geometry, road contact and tire deformation. Comput Mech 63:1165–1185MathSciNetMATH
45.
Le Beau GJ, Ray SE, Aliabadi SK, Tezduyar TE (1993) SUPG finite element computation of compressible flows with entropy and conservation variables formulations. Comput Methods Appl Mech Eng 104:397–422MATH
46.
Le Beau GJ, Tezduyar TE (1991) Finite element computation of compressible flows with the SUPG formulation. Am Soc Mech Eng Fluids Eng Div Pub FED 123:21–27
47.
Lewis JE (1967) Experimental investigation of supersonic laminar, two-dimensional boundary layer separation in a compression corner with and without cooling. Ph.D. thesis, California Institute of Technology
48.
Mazaheri A, Kleb B (2007) Exploring hypersonic, unstructured-grid issues through structured grids. In: 18th AIAA computational fluid dynamics conference
49.
Neufeld PD, Janzen AR, Aziz RA (1972) Empirical equations to calculate 16 of the transport collision integral \(\omega \) for the Lennard–Jones (12–6) potential. J Chem Phys 57(3):1100–1102
50.
Otoguro Y, Takizawa K, Tezduyar TE (2020) Element length calculation in B-spline meshes for complex geometries. Comput Mech 65:1085–1103MathSciNetMATH
51.
Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Avsar R, Zhang Y (2019) Space-time VMS flow analysis of a turbocharger turbine with isogeometric discretization: computations with time-dependent and steady-inflow representations of the intake/exhaust cycle. Comput Mech 64:1403–1419MathSciNetMATH
52.
Otoguro Y, Takizawa K, Tezduyar TE, Nagaoka K, Mei S (2019) Turbocharger turbine and exhaust manifold flow computation with the space-time variational multiscale method and isogeometric analysis. Comput Fluids 179:764–776MathSciNetMATH
53.
Saad Y, Schultz MH (1986) Gmres: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869MathSciNetMATH
54.
Shakib F, Hughes TJR, Johan Z (1991) A new finite element formulation for a computational fluid dyamics: X. The compressible Euler and Navier–Stokes equations. Comput Methods Appl Mech Eng 89:141–219
55.
Sod GA (1978) A survey of several finite difference methods for systems of nonlinear hyperbolic conservations laws. J Comput Phys 27:1–31MathSciNetMATH
56.
Sturek WB, Ray S, Aliabadi S, Waters C, Tezduyar TE (1997) Parallel finite element computation of missile aerodynamics. Int J Numer Meth Fluids 24:1417–1432MATH
57.
Szepessy A (1989) Convergence of a shock-capturing streamline diffusion finite element method for a scalar conservation law in two space dimensions. Math Comput 53(188):527–545MathSciNetMATH
58.
Tabata M (1977) A finite element approximation corresponding to the upwind finite differencing. Mem Numer Math 4:47–63MathSciNetMATH
59.
Tabata M (1978) Uniform convergence of the upwind finite element approximation for semilinear parabolic problems. J Math Kyoto Univ 18(2):327–351MathSciNetMATH
60.
Takizawa K, Tezduyar TE, Kanai T (2017) Porosity models and computational methods for compressible-flow aerodynamics of parachutes with geometric porosity. Math Models Methods Appl Sci 27:771–806MathSciNetMATH
61.
Takizawa K, Tezduyar TE, Kuraishi T (2015) Multiscale ST methods for thermo-fluid analysis of a ground vehicle and its tires. Math Models Methods Appl Sci 25:2227–2255MathSciNetMATH
62.
Takizawa K, Tezduyar TE, McIntyre S, Kostov N, Kolesar R, Habluetzel C (2014) Space-time VMS computation of wind-turbine rotor and tower aerodynamics. Comput Mech 53:1–15MATH
63.
Takizawa K, Tezduyar TE, Otoguro Y (2018) Stabilization and discontinuity-capturing parameters for space-time flow computations with finite element and isogeometric discretizations. Comput Mech 62:1169–1186MathSciNetMATH
64.
Takizawa K, Ueda Y, Tezduyar TE (2019) A node-numbering-invariant directional length scale for simplex elements. Math Models Methods Appl Sci 29:2719–2753MathSciNet
65.
Tejada-Martínez AE, Akkerman I, Bazilevs Y (2012) Large-eddy simulation of shallow water Langmuir turbulence using isogeometric analysis and the residual-based variational multiscale method. J Appl Mech 79(1):010909
66.
Tezduyar T, Aliabadi S, Behr M, Johnson A, Kalro V, Litke M (1996) Flow simulation and high performance computing. Comput Mech 18:397–412MATH
67.
Tezduyar T, Aliabadi S, Behr M, Johnson A, Mittal S (1993) Parallel finite-element computation of 3D flows. Computer 26(10):27–36MATH
68.
Tezduyar TE, Aliabadi SK, Behr M, Mittal S (1994) Massively parallel finite element simulation of compressible and incompressible flows. Comput Methods Appl Mech Eng 119:157–177MATH
69.
Tezduyar TE (2001) Adaptive determination of the finite element stabilization parameters. In: Proceedings of the ECCOMAS computational fluid dynamics conference 2001
70.
Tezduyar TE (2002) Calculation of the stabilization parameters in SUPG and PSPG formulations. In: Proceedings of the first South-American congress on computational mechanics
71.
Tezduyar TE (2003) Computation of moving boundaries and interfaces and stabilization parameters. Int J Numer Methods Fluids 43:555–575MathSciNetMATH
72.
Tezduyar TE (2004) Determination of the stabilization and shock-capturing parameters in SUPG formulation of compressible flows. In: Proceedings of European congress on computational methods in applied sciences and engineering ECCOMAS 2004
73.
Tezduyar TE (2004) Finite element methods for fluid dynamics with moving boundaries and interfaces. In: Stein E, De Borst R, Hughes TJR (eds) Encyclopedia of computational mechanics, volume 3: fluids, chapter 17. Wiley, New York
74.
Tezduyar TE (2005) Calculation of the stabilization parameters in finite element formulations of flow problems. In: Idelsohn SR, Sonzogni V (eds) Applications of computational mechanics in structures and fluids. CIMNE, Barcelona, pp 1–19
75.
Tezduyar TE, Hughes TJR (1982) Development of time-accurate finite element techniques for first-order hyperbolic systems with particular emphasis on the compressible Euler equations. NASA technical report NASA-CR-204772
76.
Tezduyar TE, Hughes TJR (1983) Finite element formulations for convection dominated flows with particular emphasis on the compressible Euler equations. In: 21st aerospace sciences meeting, AIAA paper 83-0125
77.
Tezduyar TE, Osawa Y (2000) Finite element stabilization parameters computed from element matrices and vectors. Comput Methods Appl Mech Eng 190:411–430MATH
78.
Tezduyar TE, Park YJ (1986) Discontinuity capturing finite element formulations for nonlinear convection–diffusion–reaction equations. Comput Methods Appl Mech Eng 59:307–325MATH
79.
Tezduyar TE, Senga M (2006) Stabilization and shock-capturing parameters in SUPG formulation of compressible flows. Comput Methods Appl Mech Eng 195:1621–1632MathSciNetMATH
80.
Tezduyar TE, Senga M (2007) SUPG finite element computation of inviscid supersonic flows with YZ\(\beta \) shock-capturing. Comput Fluids 36:147–159MATH
81.
Tezduyar TE, Senga M, Vicker D (2006) Computation of inviscid supersonic flows around cylinders and spheres with the SUPG formulation and YZ\(\beta \) shock-capturing. Comput Mech 38:469–481MATH
82.
83.
Xu F, Bazilevs Y, Hsu MC (2019) Immersogeometric analysis of compressible flows with application to aerodynamic simulation of rotorcraft. Math Models Methods Appl Sci 29(5):905–938MathSciNetMATH
84.
Xu F, Moutsanidis G, Kamensky D, Hsu MC, Murugan M, Ghoshal A, Bazilevs Y (2017) Compressible flows on moving domains: stabilized methods, weakly enforced essential boundary conditions, sliding interfaces, and application to gas-turbine modeling. Comput Fluids 158:201–220MathSciNetMATH
Metadaten
Titel
Stabilized methods for high-speed compressible flows: toward hypersonic simulations
verfasst von
David Codoni
Georgios Moutsanidis
Ming-Chen Hsu
Yuri Bazilevs
Craig Johansen
Artem Korobenko
Publikationsdatum
20.01.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 3/2021
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-020-01963-6

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