Some threelevel finite difference methods for simulating advection in fluids
Abstract
The onedimensional advection equation forms the basis for modeling transient forced convection in fluids. A weighted differencing on a (1, 3, 2) computational stencil is used to produce a number of finite difference equations for finding approximate solutions to this equation supplemented by smooth initialboundary conditions. Among these are several wellknown twolevel versions, as well as the leapfrog equation, the only one presently used which involves three levels in time. In addition, two recently developed and five new threelevel equations are obtained. Their accuracy has been estimated theoretically by comparing their amplitude response and relative wave speed obtained in series form using the coefficients of their modified equivalent partial differential equations. These theoretical estimates are checked by numerical tests. The results show that several of the new threelevel methods have a number of advantages when compared to those in common use, in particular having much greater accuracy when the tests involve smooth initialboundary data. Superior accuracy is retained, but to a smaller degree, when the initialboundary conditions are discontinuous.
 Publication:

Computers and Fluids
 Pub Date:
 1991
 Bibcode:
 1991CF.....19..119N
 Keywords:

 Advection;
 Computational Fluid Dynamics;
 Finite Difference Theory;
 Forced Convection;
 Boundary Conditions;
 Error Analysis;
 Partial Differential Equations;
 Wave Fronts;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer