Time‐accurate intermediate boundary conditions for large eddy simulations based on projection methods

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SUMMARYIt is well known that exact projection methods (EPM) on non-staggered grids su er for the presence of non-solenoidal spurious modes. Hence, a formulation for simulating time-dependent incompressible ows while allowing the discrete continuity equation to be satisÿed up to machine-accuracy, by using a Finite Volume-based second-order accurate projection method on non-staggered and non-uniform 3D grids, is illustrated. The procedure exploits the Helmholtz-Hodge decomposition theorem for deriving an additional velocity ÿeld that enforces the discrete continuity without altering the vorticity ÿeld. This is accomplished by ÿrst solving an elliptic equation on a compact stencil that is by performing a standard approximate projection method (APM). In such a way, three sets of divergence-free normalto-face velocities can be computed. Then, a second elliptic equation for a scalar ÿeld is derived by prescribing that its additional discrete gradient ensures the continuity constraint based on the adopted linear interpolation of the velocity. Characteristics of the double projection method (DPM) are illustrated in details and stability and accuracy of the method are addressed. The resulting numerical scheme is then applied to laminar buoyancy-driven ows and is proved to be stable and e cient.

Section: Time Integrationmentioning

confidence: 99%

Section: Setting and Discretization Of The Pressure Problem: The Apm mentioning

confidence: 99%

“…Therefore, combining (19) and (20), one rewrites Equation (17) at j while including the boundary condition (18), according to…”

Section: Setting and Discretization Of The Pressure Problem: The Apm mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A 3D second‐order accurate projection‐based Finite Volume code on non‐staggered, non‐uniform structured grids with continuity preserving properties: application to buoyancy‐driven flows

Denaro

2006

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“…Eventually, in this study the new high-order accuracy intermediate boundary conditions, proposed in References [8,28,29], are also exploited. This issue seems still leading to some misunderstanding in the literature, e.g.…”

Section: Introductionmentioning

confidence: 99%

A non‐diffusive, divergence‐free, finite volume‐based double projection method on non‐staggered grids

Aprovitola¹,

Denaro²

2006

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SUMMARYSecond-order accurate projection methods for simulating time-dependent incompressible flows on cellcentred grids substantially belong to the class either of exact or approximate projections. In the exact method, the continuity constraint can be satisfied to machine-accuracy but the divergence and Laplacian operators show a four-dimension nullspace therefore spurious oscillating solutions can be introduced. In the approximate method, the continuity constraint is relaxed, the continuity equation being satisfied up to the magnitude of the local truncation error, but the compact Laplacian operator has only the constant mode. An original formulation for allowing the discrete continuity equation to be satisfied to machine-accuracy, while using a finite volume based projection method, is illustrated. The procedure exploits the HelmholtzHodge decomposition theorem for deriving an additional velocity field that enforces the discrete continuity without altering the vorticity field. This is accomplished by solving a second elliptic field for a scalar field obtained by prescribing that its additional discrete gradients ensure discrete continuity based on the previously adopted linear interpolation of the velocity. The resulting numerical scheme is applied to several flow problems and is proved to be accurate, stable and efficient.This paper has to be considered as the companion of: 'F. M. Denaro, A 3D second-order accurate projection-based finite volume code on non-staggered, non-uniform structured grids with continuity preserving properties: application to buoyancy-driven flows. IJNMF 2006; 52(4):393-432. Now, we illustrate the details and the rigorous theoretical framework.

Using symbolic computation software packages in production of multidimensional finite volume‐based large eddy simulation codes

Aprovitola

Denaro

2012

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SUMMARY The numerical simulation of turbulence is one of the most challenging tasks in the field of the modern computational science. At present, the most advanced approach is the large eddy simulation (LES) technique wherein a formal separation between resolved (large) and unresolved (small) scales of the motion is in effect by means of a filtering operation applied onto the governing equations. However, LES requires very sophisticated numerical discretizations in terms of both accuracy and efficiency. Often, the modelling of the unresolved subgrid scale terms adds further computational complexities. This paper illustrates the suitability in using software packages for symbolic computation (in the present case, Maple© for helping in the production of subroutines for a new multidimensional, high‐order accurate finite volume‐based LES code. Specifically, it will be detailed how producing, rapidly and efficiently, the routines for computing convective, diffusive as well as subgrid scale modelling fluxes. It is particularly detailed how exploiting the package for differential calculus and linear algebra for the analytical integration of the flux polynomials over the finite volume faces. The structure of the LES code is illustrated, and an accuracy analysis of the local truncation errors is performed comparing the third‐order accurate multidimensional upwind and the classical second‐order centred reconstruction in the wavenumbers space. Then, some numerical results for the turbulent plane channel and some brief points concerning the parallelization issue are addressed. Copyright © 2012 John Wiley & Sons, Ltd.