A Taylor-Galerkin method for convective transport problems
Abstract
A method is described to derive finite element schemes for the scalar convection equation in one or more space dimensions. To produce accurate temporal differencing, the method employs forward-time Taylor series expansions including time derivatives of second- and third-order which are evaluated from the governing partial differential equation. This yields a generalized time-discretized equation which is successively discretized in space by means of the standard Bubnov-Galerkin finite element method. The technique is illustrated first in one space dimension. With linear elements and Euler, leap-frog and Crank-Nicolson time stepping, several interesting relations with standard Galerkin and recently developed Petrov-Galerkin methods emerge and the new Taylor-Galerkin schemes are found to exhibit particularly high phase-accuracy with minimal numerical damping. The method is successively extended to deal with variable coefficient problems and multi-dimensional situations.
- Publication:
-
International Journal for Numerical Methods in Engineering
- Pub Date:
- January 1984
- DOI:
- 10.1002/nme.1620200108
- Bibcode:
- 1984IJNME..20..101D
- Keywords:
-
- Computational Fluid Dynamics;
- Convective Flow;
- Galerkin Method;
- Taylor Series;
- Transport Theory;
- Crank-Nicholson Method;
- Error Analysis;
- Euler Equations Of Motion;
- Finite Element Method;
- Partial Differential Equations;
- Series Expansion;
- Fluid Mechanics and Heat Transfer