On Forward-in-Time Differencing for Fluids: Extension to a Curvilinear Framework

Open Access
Publisher Website
Google Scholar
Abstract
This paper extends the discussion of fully second-order-accurate, forward-in-time, finite-difference schemes for the advection equation with arbitrary forcing (which is viewed as a prototype for the prognostic equations of fluid dynamics) to an arbitrary curvilinear system of coordinates. Since forward-in-time schemes derive ultimately from Taylor series analysis of the uncentered-in-time differencing, it is important to include the appropriate metric terms explicitly into the algorithm's design. A rigorous truncation-error analysis leads to a compact scheme that preserves (to second-order accuracy) the consistency of Eulerian and Lagrangian formulations for fluids. Alternative approximations to the advective velocity in the transport flux are also discussed. In order to achieve second-order accuracy of the forward-in-time approximation, the advective velocity must be evaluated to at least first-order accuracy at the intermediate time level. Such a temporal staggering is usually simulated by mean... Abstract This paper extends the discussion of fully second-order-accurate, forward-in-time, finite-difference schemes for the advection equation with arbitrary forcing (which is viewed as a prototype for the prognostic equations of fluid dynamics) to an arbitrary curvilinear system of coordinates. Since forward-in-time schemes derive ultimately from Taylor series analysis of the uncentered-in-time differencing, it is important to include the appropriate metric terms explicitly into the algorithm's design. A rigorous truncation-error analysis leads to a compact scheme that preserves (to second-order accuracy) the consistency of Eulerian and Lagrangian formulations for fluids. Alternative approximations to the advective velocity in the transport flux are also discussed. In order to achieve second-order accuracy of the forward-in-time approximation, the advective velocity must be evaluated to at least first-order accuracy at the intermediate time level. Such a temporal staggering is usually simulated by mean...

This publication has 0 references indexed in Scilit: