1,721,001 research outputs found
On the application of the Helmholtz-Hodge decomposition in projection methods for the numerical solution of the incompressible Navier-Stokes equations with general boundary conditions
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An inconsistence-free integral-based dynamic one- and two-parameter mixed model
No full textThe development of the dynamic procedure as well as the deeper understanding of the link between filtering, modelling and numerics, allowed Large Eddy Simulation (LES) to make great progresses during the last years. Among several modelling approaches, the scale-similar-based modelling is based on the observation that the smallest resolved scales are the most active in the interaction with the unresolved ones. Owing to the low dissipation introduced by the scale-similar models (SSMs), the coupling with the eddy-viscosity model is often used in the so-called mixed models. Dynamic version of mixed models is historically based on the application of the test-filtering on the differential form of the filtered momentum equation. Such an approach is used for both the one and the two-coefficients mixed models. The use of the differential form of the filtered equations produces the well-known mathematical inconsistence caused by the need to extract arbitrarily the model functions out of filtering. It is known that, along with the eddy viscosity assumption, the magnitude of the Germano identity error (GIE) is strongly influenced. The mathematical inconsistence in the extraction of the dynamic eddy viscosity coefficient was recently superseded by using the new integral-based formulation. However, owing to the intrinsic limits of the Smagorinsky model, also in those results, the GIE is still remarkable therefore, the present paper presents a new formulation to the integral-based dynamic procedure for both one and two-coefficients mixed models (IDMM). The original contributions of the present paper can be summarised: (1) A theoretical analysis comparing the spectral errors for the differential and integral-based SSM, assessing that the errors are less relevant for the integral form; (2) The implementation of one and two parameters IDMM for the simulation of turbulence in a plane channel flow, assessing the reduction of the GIE and the good behaviour of the statistics that are compared with those of the other LES codes used in the LESinItaly project
On the relevance of the type of contraction of the Germano identity in the new integral-based dynamic Smagorinsky model
No full textThe 20-year old dynamic model is a well-established procedure in large eddy simulation that allowed us achieving several progresses in the field of numerical simulation of turbulence. The key of the procedure is in the derivation of the exact Germano identity, which is a tensor relation. After introducing the eddy viscosity model, in order to achieve a scalar relation and thereby determine a single value of the model constant, Germano et al. proposed contracting the tensor identity with the resolved strain rate tensor. Then, Lilly observed that this method can be efficient, but does raise the problem of indetermination when the resolved strain rate tensor cancels out. To remedy this problem, Lilly proposed calculating the model constant by a least-squares method, that is by minimizing the Germano identity error, observing that a negative value of the constant results to be consistent. Such a contraction is now a standard in the LES community, however, since the model function is arbitrarily extracted out from filtering, the necessity to adopt suitable averaging, clipping and some other cares to achieve numerically stable solutions are considered to be still open problems. Unlike the original Germano identity, which was developed in the framework of the differential formulation of the filtered equations, the recent integral-based filtered equations were shown to produce a new tensor identity wherein the model function is no longer acted on by filtering and . While the constant model preserves its full three-dimensional character, this new model was proved to produce stable and accurate solutions and is suitable also for complex flows. The aim of this study is to investigate the effects of three different contractions of the new integral-based tensor identity since each one of the projection represents a different minimization of the residual. The new expression of the Germano identity error is introduced to show the resulting accuracy in testing the turbulent flow in a plane channel. Unlike what is reported for the differential form of the dynamic model, the results highlight that the integral-based method is much less sensitive to the type of contraction than expected in the differential-based formulation. This fact confirms the better aspect of the integral-based Germano identity
Time-accurate intermediate boundary conditions for large eddy simulation based on projection methods
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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
No full textWhat does finite volume-based implicit filtering really resolve in large eddy simulations?
No full textOn the application of congruent upwind discretizations for large eddy simulations
No full textUpwind schemes were judged inappropriate for performing accurate large eddy simulations of turbulent flow owing
to the artificial dissipation that is present at high wavenumbers of the energy content. Such a conclusion has been drawn
also from some results obtained by adopting Finite Difference schemes. The present paper illustrates the performances
of some new Finite Volume upwind discretization of the convective terms in the case of the 1-D Burgers model equation
while studying the effects of numerical discretization on several Sub-Grid Scales turbulence models, starting from the
classical static and dynamic eddy viscosity models through the recent deconvolution-based ones. Basing on previously
published papers, large eddy simulations along with a deconvolution-based procedure for de-filtering the evolving
variable, have been originally developed and applied. It will be shown how the coherent application of the procedure
allows us to develop high-order accurate Finite Volume upwind schemes, which maintain a good spectral resolution
in the entire range of resolved scale. Such schemes can be candidate for performing accurate simulations of real
turbulence
Analysis of the local truncation error in the pressure-free projection method for the navier-stokes equations: a new accurate expression of the boundary conditions
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