The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON FLUID MECHANICS
Transactions ID Number: 53-550
Full Name: Ivan Kazachkov
Position: Professor
Age: ON
Sex: Male
Address: Brinellvägen, 68, Stockholm, 10044
Country: SWEDEN
Tel: 073-6860838
Tel prefix: +46
Fax:
E-mail address: Ivan.Kazachkov@energy.kth.se
Other E-mails: kazachkov@ukr.net
Title of the Paper: A combined space discrete algorithm with a Taylor series by time for solution of the non-stationary CFD problems
Authors as they appear in the Paper: Ivan V. Kazachkov
Email addresses of all the authors: Ivan.Kazachkov@energy.kth.se
Number of paper pages: 19
Abstract: 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 o!
f 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.
Keywords: Non-stationary, First Order by Time; Navier-Stokes Equations; Taylor Series; Numerical; Fractional Derivative
EXTENSION of the file: .doc
Special (Invited) Session: Numerical Methods in Fluid Mechanics
Organizer of the Session:
How Did you learn about congress: numerical method for solution of Navier-Stokes equations, non-stationary partial differential equation array, Taylor series application to solve non-stationary problem, particle moving in fluid flow and temperature distribution
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