Explicit finite difference methods for variable velocity advection in the presence of a source

The basis for modelling transient forced convection in fluids is the one-di mensional advection equation. Accurate modelling of this equation has been a topic of ongoing research for many years, particularly the development of accurate high-order finite-difference methods for the case where the advec tive velocity is constant. Unfortunately, when such a high-order finite-dif ference method is applied to the variable velocity situation, it generally degenerates at least one order. A technique is outlined which improves a re duced order formula for the constant velocity case, when it is used with a variable velocity. The method is applied to Crowley's formula which is seco nd-order when the advective velocity is constant, but only first-order in t he variable velocity case. A numerical test illustrates the increased accur acy and efficiency of two versions of the improved Crowley formula. An addi tional finite-difference formula is developed based on Lagrangian concepts. Numerical results obtained using this formula are similar in accuracy and efficiency to one of the improved versions of Crowley's formula. (C) 2000 E lsevier Science Ltd. All rights reserved.