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Stabilized Spectral Element Approximation of the Saint Venant System Using the Entropy Viscosity Technique 10th

引用

10th International Conference on Spectral and High-Order Methods (ICOSAHOM)

作者： Pasquetti, R. Guermond, J. L. Popov, B. Univ Nice Sophia Antipolis CNRS UMR 7351 Lab JA Dieudonne F-06108 Nice 2 France Univ Nice Sophia Antipolis INRIA Project CASTOR F-06108 Nice 2 France Texas A&M Univ Dept Math College Stn TX 77843 USA

ISBN: (纸本)9783319198002;9783319197999

We consider the Saint Venant system (shallow water equations), i.e. an approximation of the incompressible Euler equations widely used to describe river flows, flooding phenomena or erosion problems. We focus on problems involving dry-wet transitions and propose a solution technique using the Spectral Element Method (SEM) stabilized with a variant of the Entropy Viscosity Method (EVM) that is adapted to treat dry zones.

关键词： Entropy

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On Numerical Simulation of Transition to Turbulence in Turbine Cascade

On Numerical Simulation of Transition to Turbulence in Turbi...

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Louda, Petr Kozel, Karel Prihoda, Jaromir P. . Czech Tech Univ Karlovo Nam 13 Prague 2 Czech Republic Inst Thermomech AS CR Vvi Prague 8 Czech Republic

ISBN: (纸本)9783319257273;9783319257259

The work deals with numerical simulation of transonic turbulent flow in turbine cascades taking into account transition to turbulence. The Favre-averaged Navier-Stokes equations are closed by the SST eddy-viscosity turbulence model or by explicit algebraic Reynolds stress turbulence model (EARSM) with the gamma-zeta transition model of Lodefier and Dick. The mathematical model is solved by implicit AUSM-type finite volume method. The implementation of transition model does not require case specific input under the assumption that the whole thickness of boundary layer is contained in the same block of multi-block grid, which can easily be fulfilled in the cases considered. The results are shown for 2D tip profile turbine cascade and 2D and 3D SE1050 turbine cascade.

关键词： Finite volume method

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Finite Element Approximation of an Unsteady Projection-Based VMS Turbulence Model withWall Laws

Finite Element Approximation of an Unsteady Projection-Based...

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Chacon Rebollo, Tomas Gomez Marmol, Macarena Rubino, Samuele Univ Seville Dept Ecuac Diferenciales & Anal Numer Seville Spain Univ Seville IMUS Seville Spain

ISBN: (纸本)9783319257273;9783319257259

In this work we present the numerical analysis and study the performance of a finite element projection-based Variational MultiScale (VMS) turbulence model that includes general non-linear wall laws. We introduce Lagrange finite element spaces adapted to approximate the slip condition. The sub-grid effects are modeled by an eddy diffusion term that acts only on a range of small resolved scales. Moreover, high-order stabilization terms are considered, with the double aim to guarantee stability for coarse meshes, and help to counter-balance the accumulation of sub-grid energy together with the sub-grid eddy viscosity term. We prove stability and convergence for solutions that only need to bear the natural minimal regularity, in unsteady regime. We also study the asymptotic energy balance of the system. We finally include some numerical tests to assess the performance of the model described in this work.

关键词： Turbulence models

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C⁰ Interior Penalty Galerkin Method for Biharmonic Eigenvalue Problems 10th

引用

10th International Conference on Spectral and High-Order Methods (ICOSAHOM)

作者： Brenner, Susanne C. Monk, Peter Sun, Jiguang Louisiana State Univ Dept Math Baton Rouge LA 70803 USA Louisiana State Univ Ctr Computat & Technol Baton Rouge LA 70803 USA Univ Delaware Dept Math Sci Newark DE 19716 USA Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA

ISBN: (纸本)9783319198002;9783319197999

We consider the C-0 interior penalty Galerkin method for biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn-Hilliard type. We establish the convergence of the method and present numerical results to illustrate its performance. We also compare it with the Argyris C-1 finite element method, the Ciarlet-Raviart mixed finite element method, and the Morley nonconforming finite element method.

关键词： Galerkin methods

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A Note on the Stabilised Q₁ - P₀ Method on Quadrilaterals with High Aspect Ratios

A Note on the Stabilised Q<sub>1</sub> - P<sub>0</sub> Metho...

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Barrenechea, Gabriel R. Wachtel, Andreas Univ Strathclyde Dept Math & Stat 26 Richmond St Glasgow G1 1XH Lanark Scotland

ISBN: (纸本)9783319257273;9783319257259

This work deals with the stabilisation of mixed methods for the Stokes problem on anisotropic meshes. For this, we extend a method proposed previously in Liao and Silvester (IMA J Numer Anal 33(2):413-431, 2013), to cover the case in which the mesh contains anisotropically refined corners. This modification consists of adding extra jump terms in selected edges connecting small shape regular with large anisotropic elements. We prove stability and convergence of the proposed method, and provide numerical evidence for the fact that our approach successfully removes the dependence on the anisotropy.

关键词： Anisotropy

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Transparent Boundary Conditions for the Wave Equation: High-Order Approximation and Coupling with Characteristic NRBCs 10th

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10th International Conference on Spectral and High-Order Methods (ICOSAHOM)

作者： Sofronov, I. Dovgilovich, L. Schlumberger Moscow Russia MIPT Dolgoprudnyi Russia

ISBN: (纸本)9783319198002;9783319197999

We propose and numerically investigate two approaches for extending the application area of transparent boundary conditions (TBCs) for the wave equation: a method for generating finite-difference approximations of TBCs with the fourth and sixth order in space, and a coupling procedure of TBCs on the top boundary of a cubical computational domain with characteristic BCs at the neighbor side boundaries.

关键词： Finite difference method

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Understanding the Limits of Inf-Sup Stable Galerkin-FEM for Incompressible Flows

Understanding the Limits of Inf-Sup Stable Galerkin-FEM for ...

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Lube, Gert Arndt, Daniel Dallmann, Helene Univ Gottingen Inst Numer & Appl Math Lotzestr 16-18 D-37083 Gottingen Germany

ISBN: (纸本)9783319257273;9783319257259

The core of numerical simulations of coupled incompressible flow problems consists of a robust, accurate and fast solver for the time-dependent, incompressible Navier-Stokes equations. We consider inf-sup stable finite element methods with grad-div stabilization and symmetric stabilization of local projection type. The approach is based on a proper scale separation and only the small unresolved scales are modeled. Error estimates for the spatially discretized problem with reasonable growth of the Gronwall constant for large Reynolds numbers are given together with a critical discussion of the choice of stabilization parameters. The fast solution of the fully discretized problems (using BDF(2) in time) is accomplished via unconditionally stable velocity-pressure segregation.

关键词： Incompressible flow

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Outflow Conditions for the Navier-Stokes Equations with Skew-Symmetric Formulation of the Convective Term

Outflow Conditions for the Navier-Stokes Equations with Skew...

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Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Braack, Malte Univ Kiel Math Seminar Kiel Germany

ISBN: (纸本)9783319257273;9783319257259

The classical do-nothing condition is very often prescribed at outflow boundaries for fluid dynamical problems. However, it has a severe drawback in the context of the Navier-Stokes equations, because not even existence of weak solutions can be shown. The reason is that this boundary condition does not exhibit any control about inflow across such boundaries. This has also severe impact onto the stability of numerical algorithms for flows at higher Reynolds number. A modification of this boundary condition is one possibility to circumvent these drawbacks. This paper addresses such modifications in the context of the skew-symmetric formulation of the convective term. Moreover, we introduce a parameter which gives the possibility to downsize possible inflow even more and to enhance the stability further. Numerical examples illustrate the effectiveness of the approach.

关键词： Navier Stokes equations

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Spatial Semidiscretizations and Time Integration of 2D Parabolic Singularly Perturbed Problems

Spatial Semidiscretizations and Time Integration of 2D Parab...

引用

Conference on Boundary and Interior Layers - computational and Asymptotic Methods (BAIL)

作者： Clavero, Carmelo Carlos Jorge, Juan Univ Zaragoza Dept Appl Math C Maria Luna 3 Zaragoza Spain Univ Zaragoza IUMA Zaragoza Spain Univ Publ Navarra Dept Computat & Math Engn Pamplona Spain

ISBN: (纸本)9783319257273;9783319257259

In this work we deal with a different technique from the considered one in Clavero et al. (IMA J Numer Anal 26: 155-172, 2006;Appl NumerMath 27: 211231, 1998), to analyze the uniform convergence of some numerical methods which have been used to solve successfully two dimensional parabolic singularly perturbed problems of convection-diffusion type. For getting this, we split the discretization methods in a two stage procedure where, firstly, we semidiscretize in space, using the classical upwind scheme on a piecewise uniform Shishkin mesh, and, secondly, we integrate in time the Initial Value Problems derived from the first stage, by using the implicit Euler method. The analysis combines a suitable maximum semidiscrete principle joint to some well known techniques used in the proof of the uniform convergence of numerical schemes for elliptic singularly perturbed problems. We prove that the stiff initial value problems resulting of the spatial semidiscretization processes, have a unique solution which converges uniformly with respect to the singular perturbation parameter. Using this technique, some restrictions among the discretization parameters, which appeared in the uniform convergence analysis in Clavero et al. (Appl Numer Math 27:211-231, 1998), can be removed. Some numerical results corroborate in practice the robustness of the numerical method, according to the theoretical results.

关键词： Initial value problems

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A Reduced Integration for Reissner-Mindlin Non-linear Shell Analysis Using T-Splines 1

引用

Isogeometric Analysis and Applications 2014

作者： Adam, C. Bouabdallah, S. Zarroug, M. Maitournam, H. Ecole Polytech Lab Mecan Solides CNRS UMR 7649 Route Saclay F-91128 Palaiseau France Ecole Supr Ingn Leonard de Vinci Dept Mecan Numer & Modelisat F-92400 Courbevoie France PSA Peugeot Citroen Direct Sci & Technol Futures F-78140 Velizy Villacoublay France

ISBN: (数字)9783319233154

ISBN: (纸本)9783319233154;9783319233147

We propose a reduced shell element for Reissner-Mindlin geometric non-linear analysis within the context of T-spline analysis. The shell formulation is based on the displacements and a first order kinematic in the thickness is used for the transverse shear strains. A total Lagrangian formulation is considered for the finite transformations. The update of the incremental rotations is made using the quaternion algebra. The standard two-dimensional reduced quadrature rules for structured B-spline and NURBS basis functions are extended to the more flexible T-meshes. The non-uniform Gauss-Legendre and patchwise reduced integrations for quadratic shape functions are both presented and compared to the standard full Gauss-Legendre scheme. The performance of the element is assessed with linear and geometric non-linear two-dimensional problems in structural analysis. The effects of mesh distortion and local refinement, using both full and reduced numerical quadratures, are evaluated.

关键词： Interpolation

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