A New High Resolution TVD Scheme for Unsteady Flows with Shock Waves
DOI:
https://doi.org/10.5540/tema.2008.09.02.0311Abstract
In this work, a new high resolution TVD scheme for unsteady flows with shock waves is presented. The performance of the scheme is investigated for solving Burgers and Euler’s equations. In particular, 1D shock tubes, 1D inviscid turbulence (Burgers equation) and 2D supersonic/transonic flows are simulated.The numerical results show good agreement with numerical and experimental data.References
[1] R. Ahmed, “Numerical Schemes Applied to the Burgers and Buckley-Leverett Equations”, Msc dissertation, University of Reading, 2004.
J.D. Anderson, “Modern Compressible Flow: With Historical Perspective”, McGraw-Hill, 1990.
E.D.V. Bigarella, “Advanced Turbulence Modeling for Complex Aerospace Applications”, Ph.D. Thesis, Instituto Tecnol´ogico de Aeron´autica, S˜ao Jos´e dos Campos, SP, 2007.
V.G. Ferreira, F.A. Kurokawa, R.A.B. Queiroz,M.K. Kaibara, C.M. Oishi, J.A. Cuminato, A. Castelo, M.F. Tom´e, S. McKee, Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems, Int. J. Numer. Meth. Fluids, In Press.
V.G. Ferreira, C.M. Oishi, F.A. Kurokawa, M.K. Kaibara, J.A. Cuminato, A. Castelo, N. Mangiavacchi, M.F. Tom´e, S. McKee, A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows, Comm. Numer. Meth. Eng., 23 (2007), 419-445.
P.H. Gaskell, A.K. Lau, Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm, Int. J. Numer. Meth. Fluids, 8 (1988), 617-641.
A. Harten, High resolution schemes for conservation laws, J. Comput. Phys, 49 (1983), 357-393.
C. Hirsch, “Numerical Computation of Internal and External Flows”, Fundamentals of Numerical Discretization, John Wiley, Vol.1 and Vol.2, 1991.
A. Jameson,W. Schimidt, E. Turkel, Numerical solutions of the Euler equations by finite volume methods using Runge-Kutta time stepping schemes, AIAA J., 81 (1981), 1253-1259
B.P. Leonard, Simple high-accuracy resolution program for convective modeling of discontinuities, Int. J. Numer. Meth. Fluids, 8 (1988), 1291-1318.
NPARC Alliance Validation Archive,
http://www.grc.nasa.gov/WWW/wind/valid/raetaf/raetaf04/raetaf04.html. Access: 03/31/2008.
R.A.B. Queiroz, F.A. Kurokawa, V.G. Ferreira, F.P. Martins, Development and implementation of polynomial scheme for the numerical solution of 1D conservation laws, in “Proceedings of the VIII Simp´osio Mecˆanica Computacional”, SIMMEC, Belo Horizonte, 2008.
C.W. Shu, S. Osher, Efficient implementation of essentially non-oscillatory shock capturing schemes, J. Comput. Phys, 83 (1989), 32-78.
G. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws, J. Comput. Phys, 27 (1978), 1-31.
E.F. Toro, “Riemann Solves and Numerical Methods for Fluid Dynamics”, 2nd Edition, Springer-Verlag, Berlin, 1999.
G.D. van Albada, B. van Leer, W.W. Roberts, A comparative study of computational methods in cosmic gas dynamics, Astron. Astrophys., 108 (1982), 76-84.
P. Woodward, P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks, J. Comput. Phys, 24 (1984), 115-173.
M. Zijlema, On the construction of a third-order accurate monotone convection scheme with application to turbulent flows in general domains, Int. J. Numer. Meth. Fluids, 22 (1996), 619-641.
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