The issue of solution approximation in higher-order schemes on distorted grids

International Journal of Computational Methods

Volumn 4, Issue 2, 2007, Pages 367-382

  Petrovskaya, N B ^a   Wolkov, A V ^b  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b CENTRAL AEROHYDRODYNAMIC INSTITUTE TSAGI   (Russian Federation)

Author keywords

Discontinuous Galerkin; Distorted geometry; High order discretization; Least squares approximation; Ustructured grids

Indexed keywords

COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; GALERKIN METHODS; GRID COMPUTING;

DISCONTINUOUS GALERKIN METHOD; HIGH-ORDER DISCRETIZATION; UNSTRUCTURED GRID;

LEAST SQUARES APPROXIMATIONS;

EID: 34548717090     PISSN: 02198762     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219876207001084     Document Type: Article

References (15)

1. Agarwal, R. K. and Halt, D. W. [1999] A compact high-order unstructured grids method for the solution of Euler equations, Int. J. Num. Meth. Fluids. 31, 121-147.
2. Barth, T. and Frederickson, P. [1990] Higher-order solution of the Euler equations on unstructured grids using quadratic reconstruction, AIAA 90-0013.
3. Barth, T. J. [1998] Numerical methods for gasdynamic systems on unstructured meshes, Lecture Notes in Computer Science and Engineering 8, 195-284.
4. Bassi, F. and Rebay, S. [1997] A high-order accurate discontinuous finite element method for the numerical solution of the compressile Navier-Stokes equations, J. Comput. Phys. 131(2), 267-279.
5. Cockburn, B., Karniadakis, G. E. and Shu, C.-W. [2000] The development of discontinuous Galerkin methods, Lecture Notes in Computer Science and Engineering 11, 3-50.
6. Coirier, W. J. [1994] An adaptively refined, cartesian, cell-based scheme for the Euler and Navier-Stokes equations, PhD Thesis, University of Michigan, USA.
7. Darmofal D. L. and Haimes R. [2005] Towards the next generation in CFD, AIAA 2005-0087.
8. Hughes, T. J. R. and Brooks, A. [1979] A multidimensional upwind scheme with no crosswind diffusion, Finite Element Methods for Convection Dominated Flows, ASME, New York.
9. Mavriplis, D. J. [2003] Revisiting the least-square procedure for gradient reconstruction on unstructured meshes, AIAA 2003-3986.
10. Ollivier-Gooch, C. and Van Altena, M. [2002] A high-order-accurate unstructured mesh finite-volume scheme for the advection-diffusion equation, J. Comp. Phys. 181, 729-752.
11. Petrovskaya, N. B. [2001] Modification of a finite volume scheme for Laplace's equation, SIAM J. Sci. Comput. 23(3), 891-909.
12. Petrovskaya, N. B. [2004] The choice of weight coefficients for the least-squares gradient approximation, J. Math. Mod. 16(5), 83-93.
13. Sherwin, S. J. and Peiro, J. [2002] Mesh generation in curvilinear domains using high-order elements, Int. J. Num. Meth. Engrg. 53 207-223.
14. Venkatakrishnan, V., Allmaras, S., Kamenetskii, D. and Johnson, F. [2003] Higher order schemes for the compressible Navier-Stokes Equations, AIAA 2003-3987.
15. Vigneron, D., Vaassen, J.-M. and Essers, J. A. [2003] An implicit high order cell-centered finite volume scheme for the solution of three-dimensional Navier-Stokes equations on unstructured grids, Third MIT Conference on Computational Fluid and Solid Mechanics, MA, USA.