Analysis of accuracy and computational efficiency of the contour advection method for the barotropic vorticity equation
Keywords:
geophysical hydrodynamics, computational hydrodynamics, contour dynamics, contour advectionAbstract
The accuracy and computational efficiency of contour advection schemes for the simulation of two-dimensional inviscid incompressible flows are analyzed. Their comparison with the contour dynamics method is performed. The results obtained show that the semi-Lagrangian contour advection algorithm is very efficient when the relation of the domain size to the characteristic length of the flow is small or when the vorticity field is approximated by a large number of contours. This approach allows one to achieve a higher accuracy with an increase in computational cost.
References
- Waugh D.W., Plumb R.A. Contour advection with surgery: a technique for investigating finescale structure in tracer transport // Journal of the Atmospheric Sciences. 1994. 51, N 4. 530-540.
- Dritschel D.G., Ambaum M.H. P. A contour-advective semi-Lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields // Quarterly Journal of the Royal Meteorological Society. 1997. 123, N 540. 1097-1130.
- Dritschel D.G., Polvani L.M., Mohebalhojeh A.R. The contour-advective semi-Lagrangian algorithm for the shallow water equations // Monthly Weather Review. 1999. 127, N 7. 1151-1165.
- Macaskill C., Padden W.E. P., Dritschel D.G. The CASL algorithm for quasi-geostrophic flow in a cylinder // Journal of Computational Physics. 2003. 188, N 1. 232-251.
- Dritschel D.G, Ambaum M.H. P. The diabatic contour advective semi-Lagrangian model // Monthly Weather Review. 2006. 134, N 9. 2503-2514.
- Fontane J., Dritschel D.G. The HyperCASL algorithm: a new approach to the numerical simulation of geophysical flows // Journal of Computational Physics. 2009. 228, N 17. 6411-6425.
- Mohebalhojeh A.R., Dritschel D.G. The diabatic contour-advective semi-Lagrangian algorithms for the spherical shallow water equations // Monthly Weather Review. 2009. 137, N 9. 2979-2994.
- Dritschel D.G., Fontane J. The combined Lagrangian advection method // Journal of Computational Physics. 2010. 229, N 14, 5408-5417.
- Zabusky N.J., Hughes M.H., Roberts K.V. Contour dynamics for the Euler equations in two dimensions // Journal of Computational Physics. 1979. 30, N 1. 96-106.
- Козлов В.Ф. Метод контурной динамики в модельных задачах о топографическом циклогенезе в океане // Изв. АН СССР. Физика атмосферы и океана. 1983. 19, № 8. 845-854.
- Козлов В.Ф. Метод контурной динамики в океанологических исследованиях: результаты и перспективы // Морской гидрофизический журнал. 1985. № 4. 10-14.
- Dritschel D.G. Contour surgery: a topological reconnection scheme for extended integrations using contour dynamics // Journal of Computational Physics. 1988. 77, N 1. 240-266.
- Dritschel D.G. Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution modelling of vortex dynamics in two-dimensional, inviscid, incompressible flows // Computer Physics Reports. 1989. 10, N 3. 77-146.
- Dritschel D.G. A fast contour dynamics method for many-vortex calculations in two-dimensional flows // Physics of Fluids. 1993. 5, N 1. 173-186.
- Vosbeek P.W. C., Clercx H.J. H., Mattheij R.M. M. Acceleration of contour dynamics simulations with a hierarchical-element method // Journal of Computational Physics. 2000. 161, N 1. 287-311.
- Соколовский М.А., Веррон Ж. Динамика вихревых структур в стратифицированной вращающейся жидкости. Ижевск: Институт компьютерных исследований, 2011.
- Макаров В.Г. Вычислительный алгоритм метода контурной динамики с изменяемой топологией исследуемых областей // Моделирование в механике. 1991. 5, № 4. 83-95.
- Баранов А.А., Пермяков М.С. Ускоренный алгоритм изменения топологии для метода адвекции контуров // Вычислительные методы и программирование. 2013. 14. 75-87.
- Schaerf T.M., Macaskill C. On contour crossings in contour-advective simulations - part 1 - algorithm for detection and quantification // Journal of Computational Physics. 2012. 231, N 2. 465-480.
- Schaerf T.M., Macaskill C. On contour crossings in contour-advective simulations - part 2 - analysis of crossing errors and methods for their prevention // Journal of Computational Physics. 2012. 231, N 2. 481-504.
- Мезингер Ф., Аракава А. Численные методы, используемые в атмосферных моделях. Л.: Гидрометеоиздат, 1982.
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Published
30-05-2014
How to Cite
Баранов А., Пермяков М. Analysis of Accuracy and Computational Efficiency of the Contour Advection Method for the Barotropic Vorticity Equation // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2014. 15. 337-350
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Section 1. Numerical methods and applications