Journal ArticleDOI
High-order splitting methods for the incompressible Navier-Stokes equations
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TLDR
Improved pressure boundary conditions of high order in time are introduced that minimize the effect of erroneous numerical boundary layers induced by splitting methods, and a new family of stiffly stable schemes is employed in mixed explicit/implicit time-intgration rules.Citations
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Modeling uncertainty in flow simulations via generalized polynomial chaos
TL;DR: In this paper, the authors present a new algorithm to model the input uncertainty and its propagation in incompressible flow simulations, which is represented spectrally by employing orthogonal polynomial functionals from the Askey scheme as trial basis to represent the random space.
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An overview of projection methods for incompressible flows
TL;DR: In this paper, a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed, and the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners.
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Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations
TL;DR: Runge-Kutta-based IMEX schemes are developed that have better stability regions than the best known IMEX multistep schemes over a wide parameter range.
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Implicit-explicit methods for time-dependent partial differential equations
TL;DR: This work systematically analyze the performance of implicit-explicit IMEX schemes, propose improved new schemes, and pay particular attention to their relative performance in the context of fast multigrid algorithms and of aliasing reduction for spectral methods.
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Fourth-Order Time-Stepping for Stiff PDEs
TL;DR: A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators.
References
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Book
Spectral Methods in Fluid Dynamics
M. Y. Hussaini,Thomas A. Zang +1 more
TL;DR: Spectral methods have been widely used in simulation of stability, transition, and turbulence as discussed by the authors, and their applications to both compressible and incompressible flows, to viscous as well as inviscid flows, and also to chemically reacting flows are surveyed.
Journal ArticleDOI
Application of a Fractional-Step Method to Incompressible Navier-Stokes Equations
John Kim,Parviz Moin +1 more
TL;DR: In this paper, a numerical method for computing three-dimensional, time-dependent incompressible flows is presented based on a fractional-step, or time-splitting, scheme in conjunction with the approximate-factorization technique.
Journal ArticleDOI
A spectral element method for fluid dynamics: Laminar flow in a channel expansion
TL;DR: In this article, a spectral element method was proposed for numerical solution of the Navier-Stokes equations, where the computational domain is broken into a series of elements, and the velocity in each element is represented as a highorder Lagrangian interpolant through Chebyshev collocation points.