2004
DOI: 10.2172/975250
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Exponential integrators for the incompressible Navier-Stokes equations.

Abstract: We provide an algorithm and analysis of a high order projection scheme for time integration of the incompressible Navier-Stokes equations (NSE). The method is based on a projection onto the subspace of divergence-free (incompressible) functions interleaved with a Krylov-based exponential time integration (KBEI). These time integration methods provide a high order accurate, stable approach with many of the advantages of explicit methods, and can reduce the computational resources over conventional methods. The … Show more

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Cited by 12 publications
(10 citation statements)
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“…This method also commonly appears in the literature as the 'exponentially fitted Euler' method, for example, Hochbruck et al (1998), Newman (2003. The second scheme we choose is the third-order EPI3:…”
Section: Specific Schemesmentioning
confidence: 99%
“…This method also commonly appears in the literature as the 'exponentially fitted Euler' method, for example, Hochbruck et al (1998), Newman (2003. The second scheme we choose is the third-order EPI3:…”
Section: Specific Schemesmentioning
confidence: 99%
“…Since the nonlinear convective term in the Burgers equation is shared by the Navier-Stokes equation, the presented results give a hint of the potential of the PEBK method as an efficient parallel solver in turbulent fluid dynamics, where nonlinearity plays a key role. The question remains how to treat the pressure in the incompressible Navier-Stokes equation, which enforces the incompressibility constraint on the velocity field (see for possible approaches in [15,43]). This will be explored in future work.…”
Section: Discussionmentioning
confidence: 99%
“…The question remains how to treat the pressure in the incompressible Navier-Stokes equation, which enforces the incompressibility constraint on the velocity field (see for possible approaches in [37,131]). This will be explored in Chapter 5.…”
Section: Discussionmentioning
confidence: 99%
“…In our approach, we reformulate the governing equations without the pressure variable by applying a divergence-free projection onto the Navier-Stokes equation. The reformulated equation is an ordinary differential equation that can be integrated with a Krylov subspace method for matrix exponential functions [131,146]. We adopted the EBK method, like in Chapter 4.…”
Section: Parallelism In Timementioning
confidence: 99%
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