Burman, Erik; Garg, Deepika; Guzman, Johnny; (2023) Implicit-Explicit Time Discretization for Oseen's Equation at High Reynolds Number with Application to Fractional Step Methods. SIAM Journal on Numerical Analysis , 61 (6) pp. 2859-2886. 10.1137/23M1547573.

Preview

Text Burman_23m1547573.pdf Download (503kB) | Preview

Abstract

In this paper we consider the application of implicit-explicit (IMEX) time discretiza-tions for the incompressible Oseen equations. The pressure velocity coupling and the viscous termsare treated implicitly, while the convection term is treated explicitly. Both the second-order backwarddifferentiation and the Crank--Nicolson methods are considered for time discretization, resulting ina scheme similar to Gear's method on the one hand and to the Adams--Bashforth of second orderon the other. For the discretization in space, we consider finite element methods with stabilizationon the gradient jumps. The stabilizing terms ensures inf-sup stability for equal-order interpolationand robustness at a high Reynolds number. Under suitable Courant conditions we prove stabil-ity of Gear's scheme in this regime. The stabilization allows us to prove error estimates of order O(hk+1/2+\tau 2). Herehis the mesh parameter, kis the polynomial order, and \tau the time step. Finally we show that for inviscid flow (or underresolved viscous flow) the IMEX scheme can be written asa fractional step method in which only a mass matrix is inverted for each velocity component and aPoisson-type equation is solved for the pressure

Download activity - last month

Export as CSVJSONXML

Download activity - last 12 months

Export as XMLCSVJSON

Downloads by country - last 12 months

Export as JSONCSVXML

Archive Staff Only

View Item