The Experts below are selected from a list of 82587 Experts worldwide ranked by ideXlab platform
Yohei Morinishi - One of the best experts on this subject based on the ideXlab platform.
-
Skew-Symmetric convection Form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics, 2014Co-Authors: Yohei Morinishi, Kazuki KogaAbstract:The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-Symmetric Form have not been extended to those for moving grids. In this study, the skew-Symmetric Form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniForm flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.
-
a stable compact finite difference method with skew Symmetric Form for les of variable density flows
ASME-JSME-KSME 2011 Joint Fluids Engineering Conference: Volume 1 Symposia – Parts A B C and D, 2011Co-Authors: Kota Takeichi, Shinji Tamano, Yohei MorinishiAbstract:The objective of this study is to develop a reliable high-order numerical method for the large eddy simulation (LES) of variable density flows. To improve both the numerical accuracy and stability, we use the compact finite difference method (compact FDM) for the transport equation of compressible flows, in which the skew-Symmetric Form of the convection term is adopted. In the LES of turbulent flows, the reliability of computational results depends strongly on both the reliability of the subgrid scale (SGS) model and the accuracy of the numerical method. First, the reliability is investigated by perForming numerical simulations with unresolved grid resolution for compressible turbulent channel flows without SGS models. Then, we perForm the LES of compressible turbulent channel flows with several dynamic and non-dynamic SGS models, and compare turbulence statistics with the corresponding DNS data.Copyright © 2011 by JSME
-
skew Symmetric Form of convective terms and fully conservative finite difference schemes for variable density low mach number flows
Journal of Computational Physics, 2010Co-Authors: Yohei MorinishiAbstract:The Form of convective terms for compressible flow equations is discussed in the same way as for an incompressible one by Morinishi et al. [Y. Morinishi, T.S. Lund, O.V. Vasilyev, P. Moin, Fully conservative higher order finite difference schemes for incompressible flow, J. Comput. Phys. 124 (1998) 90], and fully conservative finite difference schemes suitable for shock-free unsteady compressible flow simulations are proposed. Commutable divergence, advective, and skew-Symmetric Forms of convective terms are defined by including the temporal derivative term for compressible flow. These Forms are analytically equivalent if the continuity is satisfied, and the skew-Symmetric Form is secondary conservative without the aid of the continuity, while the divergence Form is primary conservative. The relations between the present and existing quasi-skew-Symmetric Forms are also revealed. Commutable fully discrete finite difference schemes of convection are then derived in a staggered grid system, and they are fully conservative provided that the corresponding discrete continuity is satisfied. In addition, a semi-discrete convection scheme suitable for compact finite difference is presented based on the skew-Symmetric Form. The conservation properties of the present schemes are demonstrated numerically in a three-dimensional periodic inviscid flow. The proposed fully discrete fully conservative second-order accurate scheme is also used to perForm the DNS of compressible isotropic turbulence and the simulation of open cavity flow.
Jesse Chan - One of the best experts on this subject based on the ideXlab platform.
-
a high order discontinuous galerkin method for the Symmetric Form of the anisotropic viscoelastic wave equation
Computers & Mathematics With Applications, 2021Co-Authors: Khemraj Shukla, Jesse Chan, Maarten V De HoopAbstract:Abstract We introduce a new Symmetric treatment of anisotropic viscous terms in the viscoelastic wave equation. An appropriate memory variable treatment of stress-strain convolution terms, result into a Symmetric system of first order linear hyperbolic partial differential equations, which we discretize using a high-order discontinuous Galerkin finite element method. The accuracy of the resulting numerical scheme is verified using convergence studies against analytical plane wave solutions and analytical solutions of the viscoelastic wave equation. Computational experiments are shown for various combinations of homogeneous and heterogeneous viscoelastic media in two and three dimensions.
-
a high order discontinuous galerkin method for the Symmetric Form of the anisotropic viscoelastic wave equation
arXiv: Numerical Analysis, 2020Co-Authors: Khemraj Shukla, Jesse Chan, Maarten V De HoopAbstract:Wave propagation in real media is affected by various non-trivial physical phenomena, e.g., anisotropy, an-elasticity and dissipation. Assumptions on the stress-strain relationship are an integral part of seismic modeling and determine the deFormation and relaxation of the medium. Stress-strain relationships based on simplified rheologies will incorrectly predict seismic amplitudes, which are used for quantitative reservoir characterization. Constitutive equations for the rheological model include the generalized Hooke's law and Boltzmann's superposition principal with dissipation models based on standard linear solids or a Zener approximation. In this work, we introduce a high-order discontinuous Galerkin finite element method for wave equation in inhomogeneous and anisotropic dissipative medium. This method is based on a new Symmetric treatment of the anisotropic viscoelastic terms, as well as an appropriate memory variable treatment of the stress-strain convolution terms. Together, these result in a Symmetric system of first order linear hyperbolic partial differential equations. The accuracy of the proposed numerical scheme is proven and verified using convergence studies against analytical plane wave solutions and analytical solutions of viscoelastic wave equation. Computational experiments are shown for various combinations of homogeneous and heterogeneous viscoelastic media in two and three dimensions.
-
weight adjusted discontinuous galerkin methods matrix valued weights and elastic wave propagation in heterogeneous media
International Journal for Numerical Methods in Engineering, 2018Co-Authors: Jesse ChanAbstract:Summary Weight-adjusted inner products [1,2] are easily invertible approximations to weighted L2 inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation which is low storage, energy stable, and high order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights, with the linear elastic wave equation as an application. We present a DG Formulation of the Symmetric Form of the linear elastic wave equation, with upwind-like dissipation incorporated through simple penalty fluxes. A semi-discrete convergence analysis is given, and numerical results confirm the stability and high order accuracy of WADG for several problems in elastic wave propagation. This article is protected by copyright. All rights reserved.
-
weight adjusted discontinuous galerkin methods matrix valued weights and elastic wave propagation in heterogeneous media
arXiv: Numerical Analysis, 2017Co-Authors: Jesse ChanAbstract:Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation which is low storage, energy stable, and high order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights, with the linear elastic wave equation as an application. We present a DG Formulation of the Symmetric Form of the linear elastic wave equation, with upwind-like dissipation incorporated through simple penalty fluxes. A semi-discrete convergence analysis is given, and numerical results confirm the stability and high order accuracy of WADG for several problems in elastic wave propagation.
Kazuki Koga - One of the best experts on this subject based on the ideXlab platform.
-
Skew-Symmetric convection Form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics, 2014Co-Authors: Yohei Morinishi, Kazuki KogaAbstract:The secondary conservative finite difference method for the convective term is recognized as a useful tool for unsteady flow simulations. However, the secondary conservative convection scheme and associated skew-Symmetric Form have not been extended to those for moving grids. In this study, the skew-Symmetric Form and the secondary conservative convection schemes for ALE type moving grid simulations are proposed. For the moving grid simulations, the geometric conservation law (GCL) for metrics and the Jacobian is known as a mathematical constraint for capturing a uniForm flow. A new role of the GCL is revealed in association with the commutability and conservation properties of the convection schemes. The secondary conservative convection schemes for moving grids are then constructed for compressible and incompressible flows, respectively. For compressible flows, it is necessary to introduce a shock capturing method to resolve discontinuities. However, the shock capturing methods do not work well for turbulent flow simulations because of their excessive numerical dissipation. On the other hand, the secondary conservative finite difference method does not work well for flows with discontinuities. In this study, we also present a computational technique that combines the shock capturing and the secondary conservative finite difference methods. In order to check the commutability and conservation properties of the convection schemes, numerical tests are done for compressible and incompressible inviscid periodic flows on moving grids. Then, the reliabilities of the schemes are demonstrated on the piston problem, the flow around pitching airfoil, and the flow around an oscillating square cylinder.
Thomas Thiemann - One of the best experts on this subject based on the ideXlab platform.
-
Quantum Spin Dynamics (QSD)
Classical and Quantum Gravity, 1998Co-Authors: Thomas ThiemannAbstract:An anomaly-free operator corresponding to the Wheeler - DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor-ordering singularities and can be defined in Symmetric and non-Symmetric Form. We work in the real connection representation and obtain a well defined quantum theory. The action of the Wheeler - DeWitt constraint on spin-network states is by annihilating, creating and rerouting the quanta of angular momentum associated with the edges of the underlying graph while the ADM energy is essentially diagonalized by the spin-network states. We argue that the spin-network representation is the `nonlinear Fock representation' of quantum gravity, thus justifying the term `quantum spin dynamics (QSD)'. This paper is the first in a series of seven papers with the title `quantum spin dynamics (QSD)'.
-
quantum spin dynamics qsd
arXiv: General Relativity and Quantum Cosmology, 1996Co-Authors: Thomas ThiemannAbstract:An anomaly-free operator corresponding to the Wheeler-DeWitt constraint of Lorentzian, four-dimensional, canonical, non-perturbative vacuum gravity is constructed in the continuum. This operator is entirely free of factor ordering singularities and can be defined in Symmetric and non-Symmetric Form. We work in the real connection representation and obtain a well-defined quantum theory. We compute the complete solution to the Quantum Einstein Equations for the non-Symmetric version of the operator and a physical inner product thereon. The action of the Wheeler-DeWitt constraint on spin-network states is by annihilating, creating and rerouting the quanta of angular momentum associated with the edges of the underlying graph while the ADM-energy is essentially diagonalized by the spin-network states. We argue that the spin-network representation is the ``non-linear Fock representation" of quantum gravity, thus justifying the term ``Quantum Spin Dynamics (QSD)".
Andrea Gruber - One of the best experts on this subject based on the ideXlab platform.
-
reduced aliasing Formulations of the convective terms within the navier stokes equations for a compressible fluid
Journal of Computational Physics, 2008Co-Authors: Christopher A Kennedy, Andrea GruberAbstract:The effect on aliasing errors of different Formulations describing the cubically nonlinear convective terms within the discretized Navier-Stokes equations is examined in the presence of a non-trivial density spectrum. Fourier analysis shows that the existing skew-Symmetric Forms of the convective term result in reduced aliasing errors relative to the conservation Form. Several Formulations of the convective term, including a new Formulation proposed for cubically nonlinear terms, are tested in direct numerical simulation (DNS) of decaying compressible isotropic turbulence both in chemically inert (small density fluctuations) and reactive cases (large density fluctuations) and for different degrees of resolution. In the DNS of reactive turbulent flow, the new cubic skew-Symmetric Form gives the most accurate results, consistent with the spectral error analysis, and at the lowest cost. In marginally resolved DNS and LES (poorly resolved by definition) the new cubic skew-Symmetric Form represents a robust convective Formulation which minimizes both aliasing and computational cost while also allowing a reduction in the use of computationally expensive high-order dissipative filters.
