Type
ArticleKAUST Department
Computer Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Visual Computing Center (VCC)
Date
2019-06-24Online Publication Date
2019-06-24Print Publication Date
2019-08Embargo End Date
2020-01-01Permanent link to this record
http://hdl.handle.net/10754/656283
Metadata
Show full item recordAbstract
Finite difference schemes are widely used in applied mathematics to numerically solve partial differential equations. However, for a given solution scheme, it is usually difficult to evaluate the quality of the underlying finite difference approximation with respect to the inheritance of algebraic properties of the differential problem under consideration. In this paper, we present an appropriate quality criterion of strong consistency for finite difference approximations to systems of nonlinear partial differential equations. This property strengthens the standard requirement of consistency of difference equations with differential ones. We use a verification algorithm for strong consistency, which is based on the computation of difference Gröbner bases. This allows for the evaluation and construction of solution schemes that preserve some fundamental algebraic properties of the system at the discrete level. We demonstrate the suggested approach by simulating a Kármán vortex street for the two-dimensional incompressible viscous flow described by the Navier–Stokes equations.Citation
Michels, D. L., Gerdt, V. P., Blinkov, Y. A., & Lyakhov, D. A. (2019). On the Consistency Analysis of Finite Difference Approximations. Journal of Mathematical Sciences, 240(5), 665–677. doi:10.1007/s10958-019-04383-xSponsors
This work has been partially supported by the King Abdullah University of Science and Technology (KAUST baseline funding), the Russian Foundation for Basic Research (grant 16-01-00080), and the RUDN University Program (5-100).Additional Links
http://link.springer.com/10.1007/s10958-019-04383-xae974a485f413a2113503eed53cd6c53
10.1007/s10958-019-04383-x