Direct simulations of turbulent flow using finite-difference schemes

Mohan, Man; Moin, Parviz

doi:10.2514/6.1989-369

Cited by 105 publications

(143 citation statements)

References 8 publications

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“…Another approach, which is most similar to the one proposed in the present paper, is to introduce substantial mesh stretching in a region near the computation boundary, and to provide damping or filtering in that region to attenuate disturbances as they propagate through the layer [4,24]. The filtering technique is particularly effective because as the disturbances propagate through the stretched mesh they become progressively more poorly resolved, whereby they may be removed by a low-order discrete filter.…”

Section: Introductionmentioning

confidence: 99%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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A new buffer region (absorbing layer, sponge layer, fringe region) technique for computing compressible flows on unbounded domains is proposed. We exploit the connection between coordinate mapping from bounded to unbounded domains and filtering of the equations of motion in Fourier space in order to develop a model to damp flow disturbances (advective and acoustic) that propagate outside an arbitrarily defined near field. This effectively simulates a free-space boundary condition. Damping the solution in the far field is accomplished in a simple and effective way by applying a filter (similar to that used in large-eddy simulation) on a mesh in Fourier space, followed by a secondary filtering of the equations on the physical grid and implementation of a model for the unresolved scales. The final form of the buffer region is given in real space, independent of any discretization of the equations. Here we use a dealiased, Fourier spectral collocation method to demonstrate the efficacy of the buffer region for several model problems: acoustic wave propagation, convection of a finite-amplitude vortex, and a viscous starting jet in two dimensions. The results compare favorably to previous nonreflecting and absorbing boundary conditions.

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Section: Introductionmentioning

confidence: 99%

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

Colonius¹,

Ran

2002

Journal of Computational Physics

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“…The overall accuracy of the method is second-order in time. The explicit third-order temporal accurate Runge-Kutta procedure, coupled with an explicit high-order spatial accurate upwind bias difference scheme for the convective term, has demonstrated the highly desirable characteristic of strong numerical stability [23].…”

Section: For the General Projection Methodsmentioning

confidence: 99%

“…The Runge-Kutta method seems more suitable for the convective term because of their stability and simplicity. Rai and Moin [23] employed an explicit low-storage Runge-Kutta method, which has the additional advantage that it requires the minimum amount of computer run-time memory, for the convective term and the Crank-Nicholson technique for the diffusion term. The overall accuracy of the method is second-order in time.…”

Section: For the General Projection Methodsmentioning

confidence: 99%

A bridge between projection methods and SIMPLE type methods for incompressible Navier–Stokes equations

Abdou

2007

Numerical Meth Engineering

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SUMMARYA bridge is built between projection methods and SIMPLE type methods (Semi-Implicit Method for Pressure-Linked Equation). A general second-order accurate projection method is developed for the simulation of incompressible unsteady flows by employing a non-linear update of pressure term aswhere n is a coefficient matrix, which may depend on the grid size, time step and even velocity. It includes three-and four-step projection methods. The standard SIMPLE method is written in a concise formula for steady and unsteady flows. It is proven that SIMPLE type methods have second-order temporal accuracy for unsteady flows. The classical second-order projection method and SIMPLE type methods are united within the framework of the general second-order projection formula. Two iteration algorithms of SIMPLE type methods for unsteady flows are described and discussed. In addition, detailed formulae are provided for general projection methods by using the Runge-Kutta technique to update the convective term and Crank-Nicholson scheme for the diffusion term.

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“…Matrix-free stencil operators based on explicit finite difference schemes are widely used in industry and academic research, although they merely represent one of many approaches to solving PDEs [Baba16], [Liu09], [Rai91]. In this paper we therefore limit our discussion of numerical methods and instead focus on the ease with which these operators can be created symbolically.…”

Section: Introductionmentioning

confidence: 99%

Optimised finite difference computation from symbolic equations

Lange¹,

Kukreja²,

Luporini³

et al. 2017

Proceedings of the 16th Python in Science Conference

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Abstract-Domain-specific high-productivity environments are playing an increasingly important role in scientific computing due to the levels of abstraction and automation they provide. In this paper we introduce Devito, an opensource domain-specific framework for solving partial differential equations from symbolic problem definitions by the finite difference method. We highlight the generation and automated execution of highly optimized stencil code from only a few lines of high-level symbolic Python for a set of scientific equations, before exploring the use of Devito operators in seismic inversion problems.

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Direct simulations of turbulent flow using finite-difference schemes

Cited by 105 publications

References 8 publications

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

A Super-Grid-Scale Model for Simulating Compressible Flow on Unbounded Domains

A bridge between projection methods and SIMPLE type methods for incompressible Navier–Stokes equations

Optimised finite difference computation from symbolic equations

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