A simple high-resolution advection scheme

International Journal for Numerical Methods in Fluids

Volumn 56, Issue 5, 2008, Pages 469-484

  Mingham, C G ^a   Causon, D M ^a  

^a MANCHESTER METROPOLITAN UNIVERSITY   (United Kingdom)

Author keywords

Advection; Finite volume; Numerical; Riemann; Time marching

Indexed keywords

ALGORITHMS; FINITE VOLUME METHOD; INTERPOLATION; RUNGE KUTTA METHODS;

CELL INTERFACE FLUX; PREDICTOR-CORRECTOR SEQUENCE; REIMANN PROBLEM;

ADVECTION;

ADVECTION; ALGORITHMS; FINITE VOLUME METHOD; INTERPOLATION; RUNGE KUTTA METHODS;

EID: 38949140913     PISSN: 02712091     EISSN: 10970363     Source Type: Journal    
DOI: 10.1002/fld.1536     Document Type: Article

References (25)

1. Chen Y, Falconer RA. Advection-diffusion modelling using the modified QUICK scheme. International Journal for Numerical Methods in Fluids 1992; 15:1171-1196.
2. Hirt CW, Nichols BD. Volume of fluid (VOF) method for dynamics of free boundaries. Journal of Computational Physics 1981; 39:201-225.
3. Osher S, Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. Journal of Computational Physics 1999; 79:12-49.
4. Falconer RA. Flow and water quality modelling in coastal and inland waters. Journal of Hydraulic Research 1992; 30:437-452.
5. Bott A. A positive definite advection scheme obtained by nonlinear renormalization of the advective fluxes. Monthly Weather Review 1989; 117:1006-1015.
6. Birman A, Har'El NY, Falcovitz J, Ben-Artzi M, Feldman U. Operator-split computation of 3D symmetric flow. Twenty-second International Symposium on Shock Waves, Southampton, U.K., 1999, paper 3461.
7. Giraldo FX, Neta B. A comparison of a family of Eulerian and semi-Lagrangian finite element methods for the advection-diffusion equation. Computer Modelling of Seas and Coastal Regions 3 - Coastal 97. La Coruna: Spain, 1997; ISBN 1-85312-4990.
8. Manson JR, Wallis SG. An accurate numerical algorithm for advective transport. Communications in Numerical Methods in Engineering 1995; 11:1039-1045.
9. Yeh GT. A Lagrangian-Eulerian method with zoomable hidden fine-mesh approach to solving advection-dispersion equations. Water Resources Research 1990; 26:1133-1144.
10. Carmichael GR, Peters LK, Kitada T. A second generation model for region-scale transport/chemistry/deposition. Atmospheric Environment 1986; 20:173-188.
11. Li CW. Least square-characteristics and finite elements for advection-dispersion simulation. International Journal for Numerical Methods in Engineering 1990; 29:1343-1364.
12. Van Leer B. Towards the ultimate conservative difference scheme II: monotonicity and conservation combined in a single scheme. Journal of Computational Physics 1974; 14:361-370.
13. Borthwick AGL, Barber RW. The River and reservoir flow modelling using the transformed shallow water equations. International Journal for Numerical Methods in Fluids 1996; 14:1193-1217.
14. Barber RW, Pearson RV. Modelling tide-induced currents and pollutant transport using a generalised curvilinear co-ordinate system. Proceedings of the 1st International Conference on Environmental Problems in Coastal Regions, Rio, Brasil. Wessex Institute of Technology: U.K., 1996; 263-274.
15. Yang G, Causon DM, Ingram DM, Saunders R, Batten P. A Cartesian cut cell method for compressible flows - Part A: static body problems. Aeronautical Journal 1997; 101(1002):47-56.
16. Yang G, Causon DM, Ingram DM, Saunders R, Batten P. A Cartesian cut cell method for compressible flows - Part B: moving body problems. Aeronautical Journal 1997; 101(1002):57-65.
17. Strang G. On the construction and comparison of finite difference schemes. SIAM Journal on Numerical Analysis 1968; 5:506-517.
18. Valocchi AJ, Malmstead M. Accuracy of operator splitting for advection-dispersion reaction problems. Water Resources Research 1992; 28(5):1471-1476.
19. Van Leer B. On the relation between the upwind differencing schemes of Godunov, Enquist-Osher and Roe. SIAM Journal on Scientific and Statistical Computing 1984; 5(1):1-20.
20. Toro E. Riemann Solvers and Numerical Methods for Fluid Dynamics. Springer: Berlin, 1997.
21. Leveque RJ. Numerical Methods for Conservation Laws. Birkhauser: Basel, 1994; 101. ISBN 3-8176-2723-5.
22. MacCormack RW. The effect of hypervelocity impact cratering. AIAA Paper No. 69-354, 1969.
23. Mingham CG, Causon DM, Ingram DM. A TVD MacCormack scheme for transcritical flow. Proceedings of the ICE: Water and Maritime Engineering 2001; 148(3):167-175. ISSN 1472-4561.
24. Leonard BR Simple high-accuracy resolution program for convective modelling of discontinuities. International Journal for Numerical Methods in Fluids 1988; 8(10):1291-1318.
25. Tamamidis P, Assanis DN. Evaluation of various high-order-accuracy schemes with and without flux limiters. International Journal for Numerical Methods in Fluids 1993; 16:931-948.