A comparison study on multivariant and univariant finite elements for three-dimensional incompressible viscous flows

1995 ◽  
Vol 21 (8) ◽  
pp. 683-696 ◽  
Author(s):  
Tony W. H. Sheu ◽  
Morten M. T. Wang
Keyword(s):  
Finite Elements ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Comparison Study ◽  
Incompressible Viscous Flows

Exponential Time Differencing Gauge Method for Incompressible Viscous Flows

2017 ◽  
Vol 22 (2) ◽  
pp. 517-541 ◽  
Author(s):  
Lili Ju ◽  
Zhu Wang
Keyword(s):  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Viscous Flows ◽  
Momentum Equation ◽  
Compact Representation ◽  
Kinematic Equation ◽  
Exponential Time ◽  
Exponential Time Differencing ◽  
Incompressible Viscous Flows

AbstractIn this paper, we study an exponential time differencing method for solving the gauge system of incompressible viscous flows governed by Stokes or Navier-Stokes equations. The momentum equation is decoupled from the kinematic equation at a discrete level and is then solved by exponential time stepping multistep schemes in our approach. We analyze the stability of the proposed method and rigorously prove that the first order exponential time differencing scheme is unconditionally stable for the Stokes problem. We also present a compact representation of the algorithm for problems on rectangular domains, which makes FFT-based solvers available for the resulting fully discretized system. Various numerical experiments in two and three dimensional spaces are carried out to demonstrate the accuracy and stability of the proposed method.

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