A combined space discrete algorithm with a taylor series by time for solution of the non-stationary CFD problems
2011 (English)In: WSEAS Transactions on Fluid Mechanics, ISSN 1790-5087, Vol. 6, no 1, 51-69 p.Article in journal (Refereed) Published
The first order by time partial differential equation (PDE) is used as models in applications such as fluid flow, heat transfer, solid deformation, electromagnetic waves, and many others. In this paper we propose the new numerical method to solve a class of the initial-boundary value problems for the PDE using any known space discrete numerical schemes and a Taylor series expansion by time. Derivatives by time are got from the outgoing PDE and its further differentiation (for second and higher order derivatives by time). By numerical solution of the PDE and PDE arrays normally a second order discretization by space is applied while a first order by time is sometimes satisfactory too. Nevertheless, in a number of different problems, discretization both by temporal and by spatial variables is needed of highest orders, which complicates the numerical solution, in some cases dramatically. Therefore it is difficult to apply the same numerical methods for the solution of some PDE arrays if their parameters are varying in a wide range so that in some of them different numerical schemes by time fit the best for precise numerical solution. The Taylor series based solution strategy for the non-stationary PDE in CFD simulations has been proposed here that attempts to optimise the computation time and fidelity of the numerical solution. The proposed strategy allows solving the non-stationary PDE with any order of accuracy by time in the frame of one algorithm on a single processor, as well as on a parallel cluster system. A number of examples considered in this paper have shown applicability of the method and its efficiency.
Place, publisher, year, edition, pages
2011. Vol. 6, no 1, 51-69 p.
First order by time, Fractional derivative, Navier-stokes equations, Non-stationary, Numerical, Taylor series
IdentifiersURN: urn:nbn:se:kth:diva-151240ScopusID: 2-s2.0-80051614114OAI: oai:DiVA.org:kth-151240DiVA: diva2:747207
QC 201409162014-09-162014-09-152014-09-16Bibliographically approved