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Nonlinear Elasticity for Mesh Deformation with High-Order Discontinuous Galerkin Methods for the Navier-Stokes Equations on Deforming Domains 10th

引用

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

作者： Froehle, Bradley Persson, Per-Olof Univ Calif Berkeley Dept Math Berkeley CA 94720 USA

ISBN: (纸本)9783319198002;9783319197999

We present a numerical framework for simulation of the compressible Navier-Stokes equations on problems with deforming domains where the boundary motion is prescribed by moving meshes. Our goal is a high-order accurate, efficient, robust, and general purpose simulation tool. To obtain this, we use a discontinuous Galerkin space discretization, diagonally implicit Runge-Kutta time integrators, and fully unstructured meshes of triangles and tetrahedra. To handle the moving boundaries, a mapping function is produced by first deforming the mesh using a neo-Hookean elasticity model and a high-order continuous Galerkin FEM method. The resulting nonlinear equations are solved using Newton's method and a robust homotopy approach. From the deformed mesh, we compute grid velocities and deformations that are consistent with the time integration scheme. These are used in a mapping-based arbitrary Lagrangian-Eulerian formulation, with numerically computed mapping Jacobians which satisfy the geometric conservation law. We demonstrate our methods on a number of problems, ranging from model problems that confirm the high-order accuracy to the flow in domains with complex deformations.

关键词： Mapping

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Numerical Dissipation Control in High Order Shock-Capturing Schemes for LES of Low Speed Flows 10th

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

作者： Kotov, D. V. Yee, H. C. Wray, A. A. Sjoegreen, B. Bay Area Environm Res Inst Petaluma CA 94952 USA NASA Ames Res Ctr Moffett Field CA 94035 USA Lawrence Livermore Natl Lab Livermore CA 94551 USA

ISBN: (纸本)9783319198002;9783319197999

In Kotov et al. (Proceedings of ICCFD8, 2014) the LES of a turbulent flow with a strong shock by Yee and Sjogreen (Proceedings of ICOSAHOM 09, Trondheim, Norway, 2013) scheme indicated a good agreement with the filtered DNS data. There are vastly different requirements in the minimization of numerical dissipation for accurate turbulence simulations of different compressible flow types and flow speeds. The present study examines the versatility of the Yee and Sjgreen scheme for LES of low speed flows. Special attention is focused on the accuracy performance of this scheme using the Smagorinsky and the Germano-Lilly SGS models.

关键词： Shear flow

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Domain Decomposition Methods and Kirchhoff-Love Shell Multipatch Coupling in Isogeometric Analysis 1

引用

Isogeometric Analysis and Applications 2014

作者： Apostolatos, Andreas Breitenberger, Michael Wuechner, Roland Bletzinger, Kai-Uwe Tech Univ Munich Arcisstr 21 D-80333 Munich Germany

ISBN: (数字)9783319233154

ISBN: (纸本)9783319233154;9783319233147

The necessity for solving the isogeometric Kirchhoff-Love shell problem into multiple domains has been exemplified especially in cases where the geometry comprises multipatches. In fact, geometries taken from Computer Aided Geometric Design involve in principle trimmed multipatches. Herein, the application and comparison of the most common Domain Decomposition Methods for the coupling of Kirchhoff-Love shell multipatches in isogeometric analysis is presented. The investigated methods comprise Penalty and Lagrange Multipliers methods. All methods are extended to account for geometrically nonlinear problems. The aforementioned methods provided highly accurate results, thus extending the Kirchhoff-Love shell analysis from a single to multiple patches which is a prerequisite for solving practical engineering problems using isogeometric analysis.

关键词： Domain decomposition methods

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3D Viscoelastic Anisotropic Seismic Modeling with High-Order Mimetic Finite Differences 10th

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

作者： Ferrer, Miguel de la Puente, Josep Farres, Albert Castillo, Jose E. Barcelona Supercomp Ctr Comp Applicat Sci & Engn Barcelona 08034 Spain San Diego State Univ Computat Sci Res Ctr San Diego CA 92182 USA

ISBN: (纸本)9783319198002;9783319197999

We present a scheme to solve three-dimensional viscoelastic anisotropic wave propagation on structured staggered grids. The scheme uses a fully-staggered grid (FSG) or Lebedev grid (Lebedev, J Sov Comput Math Math Phys 4: 449-465, 1964;Rubio et al. Comput Geosci 70: 181-189, 2014), which allows for arbitrary anisotropy as well as grid deformation. This is useful when attempting to incorporate a bathymetry or topography in the model. The correct representation of surface waves is achieved by means of using high-order mimetic operators (Castillo and Grone, SIAM J Matrix Anal Appl 25: 128-142, 2003;Castillo and Miranda, Mimetic discretization methods. CRC Press, Boca Raton, 2013), which allow for an accurate, compact and spatially high-order solution at the physical boundary condition. Furthermore, viscoelastic attenuation is represented with a generalized Maxwell body approximation, which requires of auxiliary variables to model the convolutional behavior of the stresses in lossy media. We present the scheme's accuracy with a series of tests against analytical and numerical solutions. Similarly we show the scheme's performance in high-performance computing platforms. Due to its accuracy and simple pre-and post-processing, the scheme is attractive for carrying out thousands of simulations in quick succession, as is necessary in many geophysical forward and inverse problems both for the industry and academia.

关键词： Surface waves

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Blow-Up of Solutions and Interior Layers in a Caputo Two-Point Boundary Value Problem

Blow-Up of Solutions and Interior Layers in a Caputo Two-Poi...

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

作者： Stynes, Martin Luis Gracia, Jose Beijing Computat Sci Res Ctr Div Appl Math Beijing Peoples R China Natl Univ Ireland Dept Math Cork Ireland Univ Zaragoza Inst Math & Applicat Dept Appl Math Zaragoza Spain

ISBN: (纸本)9783319257273;9783319257259

A two-point boundary value problem whose highest-order term is a Caputo fractional derivative of order delta epsilon (1,2) is considered on the interval OE [0, 1]. It is asserted in the published literature that the solutions of such problems can exhibit a boundary layer at x = 1 as delta -> 1(+)when the convection coefficient b satisfies max(x epsilon[0,1]) b(x) >= 1. It will be shown here that for constant b a boundary layer can appear in the case b > 1 but in the case b = 1 the behaviour of the solution is substantially different. Furthermore, a numerical example is given to show that for certain b(x) the solution can exhibit an interior layer-a phenomenon that has not previously been reported in the research literature.

关键词： Boundary layers

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Difference Schemes of High Accuracy Order on Uniform Grids for a Singularly Perturbed Parabolic Reaction-Diffusion Equation

Difference Schemes of High Accuracy Order on Uniform Grids f...

引用

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

作者： Shishkina, Lidia Russian Acad Sci Inst Math & Mech Ekaterinburg Russia

ISBN: (纸本)9783319257273;9783319257259

For a singularly perturbed parabolic reaction-diffusion equation with a perturbation parameter epsilon (epsilon epsilon (0, 1]) multiplying the highest-order derivative, we consider a technique to construct epsilon-uniformly convergent in the maximum norm difference schemes of higher accuracy order on uniform grids. In constructing such schemes, we use the solution decomposition method, in which grid approximations of the regular and singular components in the solution are considered on uniform grids. Increasing of the convergence rate of the scheme constructed with improved accuracy of order O (N-4 ln(4) N + N-0(-2)) where N and N-0 are the number of nodes in the meshes in x and t, respectively, is achieved using a Richardson extrapolation technique applied to the regular and singular components. In the proposed Richardson technique, when constructing embedded grids we use most dense grids as main grids. This approach allows us to construct schemes that converge epsilon-uniformly in the maximum norm at the rate O (N-6 ln(6) N + N-0(-3)) and higher.

关键词： Perturbation techniques

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On the Application of Algebraic Flux Correction Schemes to Problems with Non-vanishing Right-Hand Side

On the Application of Algebraic Flux Correction Schemes to P...

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

作者： Knobloch, Petr Charles Univ Prague Fac Math & Phys Dept Numer Math Sokolovska 83 Prague 18675 8 Czech Republic

ISBN: (纸本)9783319257273;9783319257259

It is demonstrated that the application of an algebraic flux correction (AFC) scheme to a singularly perturbed steady convection-diffusion equation with a non-vanishing right-hand side does not lead to satisfactory results in the boundary layer region. It is proved that it is not possible to construct an AFC scheme of the type considered for which the solution is accurate in the whole computational domain for any convection-diffusion problem with non-vanishing right-hand side.

关键词： Perturbation techniques

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Multilevel Preconditioning for Variational Problems 1

引用

Isogeometric Analysis and Applications 2014

作者： Kunoth, Angela Univ Cologne Math Inst Weyertal 86-90 D-50931 Cologne Germany

ISBN: (数字)9783319233154

ISBN: (纸本)9783319233154;9783319233147

For the numerical solution of linear variational problems involving elliptic partial differential operators in n >= 2 space dimensions, iterative solution schemes are indispensable on account of their problem size. Our guiding principle is to devise iterative solvers which are optimal in the number of arithmetic operations, i.e., which are of linear complexity in the total number of unknowns. For these algorithms, asymptotically optimal preconditioners are required. The class of preconditioners for which this can be shown are of multilevel type, requiring nested approximation spaces to approximate the solution of the system on a fine user-specified grid. For smooth solutions of standard second and fourth order elliptic PDEs (partial differential equations) in variational form, approximations based on tensor products of higher-order B-splines yield high accuracy. For such problem classes, this survey collects the main ingredients for multilevel preconditioners in terms of higher order B-splines. There are three types of multilevel preconditioners for which asymptotic optimality can be shown. Two of them, the so-called additive preconditioners, are specified for isogeometric analysis involving linear elliptic partial differential operators in terms of variants of the BPX (Bramble-Pasciak-Xu) preconditioner and wavelet preconditioners. The third class are the so-called multiplicative preconditioners, specifically, multigrid methods. An essential ingredient for all these multilevel preconditioners are intergrid operators which transform vectors or matrices between grids of different grid spacing. For higher order B-splines, these intergrid operators can be derived from their refinement relations. In addition to a presentation of the theoretical ingredients, the performance of the different preconditioners will be demonstrated by some numerical examples.

关键词： Interpolation

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Higher Order Quasi Monte-Carlo Integration in Uncertainty Quantification 10th

引用

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

作者： Dick, Josef Quoc Thong Le Gia Schwab, Christoph UNSW Australia Sch Math & Stat Sydney NSW Australia ETH Seminar Appl Math CH-8092 Zurich Switzerland

We review recent results on dimension-robust higher order convergence rates of Quasi-Monte Carlo Petrov-Galerkin approximations for response functionals of infinite-dimensional, parametric operator equations which ari... 详细信息

ISBN: (纸本)9783319198002;9783319197999

关键词： Uncertainty analysis

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On the Delay and Inviscid Nature of Turbulent Break-Away Separation in the High-Re Limit

On the Delay and Inviscid Nature of Turbulent Break-Away Sep...

引用

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

作者： Scheichl, Bernhard Vienna Univ Technol Inst Fluid Mech & Heat Transfer Tower BA-E322Getreidemarkt 9 A-1060 Vienna Austria AC2T Res GmbH Austrian Ctr Competence Tribol A-2700 Wiener Neustadt Austria

ISBN: (纸本)9783319257273;9783319257259

We complement the recently achieved status quo of a self-consistent asymptotic theory: incompressible-flow separation from the perfectly smooth surface of a bluff rigid obstacle that perturbs an otherwise uniform flow in an unbounded domain. Here the globally formed Reynolds number, Re, takes on arbitrarily large values, and we are concerned with a long-standing challenge in boundary layer theory. Specifically, the external flow is sought in the class of potential flows with free streamlines, and the level of turbulence intensity, concentrated in the boundary layer undergoing separation, is measured in terms of distinguished limits. Their particular choices categorise the type of the viscous-inviscid interaction mechanism governing local separation and the strength of its downstream delay when compared with laminar-flow separation. In the case of extreme retardation, this implies the selection of a fully attached potential flow around a closed body, the singular member of the family of free-streamline flows. In turn, the asymptotic theory predicts the distance of the separation from the thus emerging rear stagnation point or trailing edge of the body to vanish at a rate much weaker than that given by 1/ ln Re, which plays a crucial role in the scaling of firmly attached turbulent boundary layers. Notably, the overall theory only resorts to specific turbulence closures when it comes to numerical v investigations.

关键词： Reynolds number

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