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

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