Contour Dynamics with Symplectic Time Integration

✍ Scribed by P.W.C. Vosbeek; R.M.M. Mattheij

• Book ID: 102586649
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 498 KB
• Volume: 133
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1997.5668

✦ Synopsis

Here u is the component of the velocity field in the x-direction and v the component in the y-direction. From

In this paper we consider the time evolution of vortices simulated by the method of contour dynamics. Special attention is being paid this we can see that we are dealing with a Hamiltonian to the Hamiltonian character of the governing equations and in system with Hamiltonian Ϫ. A very important property particular to the conservational properties of numerical time integraof such a system is the concept of preservation of area (see tion for them. We assess symplectic and nonsymplectic schemes. [10]) which in our case is equivalent to conservation of For the former methods, we give an implementation which is both mass. Operators which have this property, are called symefficient and yet effectively explicit. A number of numerical examplectic. The solution operator of a Hamiltonian system is ples sustain the analysis and demonstrate the usefulness of the approach. ᮊ 1997 Academic Press thus a symplectic operator. Since we like to solve this Hamiltonian system numerically, it is important, especially for long-time calculations, to preserve the area. This is