Nonmonotone chemotactic invasion: High-resolution simulations, phase plane analysis and new benchmark problems

Journal of Computational Physics

Volumn 225, Issue 1, 2007, Pages 6-12

  Simpson, Matthew J ^a   Landman, Kerry A ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Chemotaxis; High resolution methods; Hyperbolic conservation law; Invasion; Shocks

Indexed keywords

BENCHMARK PROBLEMS; CHEMOTAXI; HIGH RESOLUTION SIMULATIONS; HIGH-RESOLUTION METHODS; HYPERBOLIC CONSERVATION LAWS; INVASION; NONMONOTONE; PHASE-PLANE ANALYSIS; SHOCK;

BIOCHEMISTRY;

EID: 34447253569     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2007.03.016     Document Type: Article

References (23)

1. Burggraf O.R. Analytical and numerical studies of the structure of steady separated flows. J. Fluid Mech. 24 (1966) 113-151
2. M.A. Christon, D.I. Ketcheson, A.C. Robinson, An assessment of semi-discrete central schemes for hyperbolic conservation laws, SANDIA National Laboratories Report. SAND2003-3238, 2003.
3. Donea J., and Huerta A. Finite Element Methods for Flow Problems (2003), John Wiley and Sons, West Sussex, England
4. Courant R., and Hilbert D. Methods of Mathematical Physics. 2nd ed. vol. 2 (1964), Interscience, New York
5. H.R. Henry, Effects of dispersion on salt encroachment in coastal aquifers. In Sea Water in Coastal Aquifers, US Geological Survey Supply Paper 1613-C: 70-84, 1964.
6. Kurganov A., and Tadmor E. New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comp. Phys. 160 (2000) 241-282
7. Landman K.A., Simpson M.J., Slater J.L., and Newgreen D.F. Diffusive and chemotactic cellular migration: Smooth and discontinuous travelling wave solutions. SIAM J. Appl. Math. 65 (2005) 1420-1442
8. K.A. Landman, M.J. Simpson, G.J. Pettet, Nonmonotonic tactic travelling waves. Submitted for publication.
9. Le Bars M., and Grae Worster M. Solidification of a binary alloy: Finite-element single-domain simulation and new benchmark solutions. J. Comp. Phys. 216 (2006) 247-263
10. LeVeque R.J. Finite volume methods for hyperbolic problems (2002), Cambridge University Press, Cambridge, United Kingdom
11. McOwen R.C. Partial Differential Equations. 3rd ed. (1996), Prentice Hall, NJ
12. Oberkampf W.L., and Trucano T.F. Verification and validation in computational fluid dynamics. Prog. Aerosp. Sci. 38 (2002) 209-272
13. Oreskes N., Shrader-Frechette K., and Belitz K. Verification, validation and confirmation of numerical models in the earth sciences. Science 263 (1994) 641-646
14. Pelanti M., and LeVeque R.J. High-resolution finite volume methods for dusty gas jets and plumes. SIAM J. Sci. Comput. 28 (2006) 1335-1360
15. Perumpanani A.J., Sherratt J.A., Norbury J., and Byrne H.M. A two parameter family of travelling waves with a singular barrier from the modelling of extracellular matrix mediated cellular invasion. Physica D 126 (1999) 145-159
16. Pettet G.J., McElwain D.L.S., and Norbury J. Lotka-Volterra equations with chemotaxis: Walls barriers and chemotaxis. IMA J. Math. Appl. Med. 17 (2000) 395-413
17. Price D.J., and Monaghan J.J. Smoothed particle magnetohydrodynamics - I: Algorithm tests in one dimension. Mon. Not. R Astron. Soc. 348 (2004) 123-138
18. Simmons C.T., Narayan K.A., and Wooding R.A. On a test case for density dependent groundwater flow and solute transport models: the salt lake problem. Water Resour. Res. 35 (1999) 3607-3620
19. Simpson M.J., and Clement T.P. Improving the worthiness of the Henry problem as a benchmark for density-dependent groundwater flow models. Water Resour. Res. 40 (2004) W01504 10.1029/2003WR002199
20. Simpson M.J., Landman K.A., and Newgreen D.F. Chemotactic and diffusive migration on a non-uniformly growing domain: Numerical algorithm development and applications. J. Comput. Appl. Math. 192 (2006) 282-300
21. Sod G.A. A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws. J. Comp. Phys. 27 (1978) 1-31
22. Wooding R.A. Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. J. Fluid Mech. 39 (1969) 195-477
23. Ying X., Khan A.A., and Wang S.S.Y. Upwind conservative scheme for the Saint Venant equations. J. Hydraul. Eng. - ASCE 130 (2004) 977-987