The Experts below are selected from a list of 246 Experts worldwide ranked by ideXlab platform
Thomas J R Hughes - One of the best experts on this subject based on the ideXlab platform.
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a space time galerkin least squares finite element formulation of the navier stokes Equations for moving domain problems
Computer Methods in Applied Mechanics and Engineering, 1997Co-Authors: Arif Masud, Thomas J R HughesAbstract:A space-time Galerkin/least-squares finite element formulation of the Navier-Stokes Equations is presented for the analysis of free surface flows, moving spatial configurations and deforming fluid-structure interfaces. The Variational Equation is based on the time discontinuous Galerkin method employing the physical entropy variables. The space-time elements are oriented in time to accommodate the spatial deformations. If the elements are oriented along the particle paths, the formulation is Lagrangian and if they are fixed in time, it is Eulerian. Consequently this formulation is analogous to the arbitrary Lagrangian-Eulerian (ALE) technique. A novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration. Numerical results are presented to show the performance of the method.
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A new finite element formulation for computational fluid dynamics. X - The compressible Euler and Navier-Stokes Equations
Computer Methods in Applied Mechanics and Engineering, 1991Co-Authors: Fahim Shakib, Thomas J R Hughes, Zdeněk JohanAbstract:A space-time element method is presented for solving the compressible Euler and Navier-Stokes Equations. The proposed formulation includes the Variational Equation, predictor multi-corrector algorithms and boundary conditions. The Variational Equation is based on the time-discontinuous Galerkin method, in which the physical entropy variables are employed. A least-squares operator and a discontinuity-capturing operator are added, resulting in a high-order accurate and unconditionally stable method. Implicit/explicit predictor multi-corrector algorithms, applicable to steady as well as unsteady problems, are presented; techniques are developed to enhance their efficiency. Implementation of boundary conditions is addressed; in particular, a technique is introduced to satisfy nonlinear essential boundary conditions, and a consistent method is presented to calculate boundary fluxes. Numerical results are presented to demonstrate the performance of the method.
Peter M. Pinsky - One of the best experts on this subject based on the ideXlab platform.
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a space time finite element method for structural acoustics in infinite domains part 2 exact time dependent non reflecting boundary conditions
Computer Methods in Applied Mechanics and Engineering, 1996Co-Authors: Lonny L. Thompson, Peter M. PinskyAbstract:Abstract In Part 1, a new space-time finite element method for transient structural acoustics in exterior domains was given. The formulation employs a finite computational fluid domain surrounding the structure and incorporates local time-dependent non-reflecting boundary conditions on the fluid truncation boundary. In this paper, new exact time-dependent non-reflecting boundary conditions are developed for solutions of the scalar wave Equation in three space dimensions. These high-order accurate absorbing boundary conditions are based on the exact impedance relation for the acoustic fluid through the Dirichlet-to-Neumann (DtN) map in the frequency domain and are exact for solutions consisting of the first N spherical wave harmonics. Time-dependent boundary conditions are obtained through an inverse Fourier transform procedure. Two alternative sequences of boundary conditions are derived; the first involves both temporal and spatial derivatives (local in time and local in space version), and the second involves temporal derivatives and a spatial integral (local in time and non-local in space version). These non-reflecting boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time Variational Equation, i.e. they are enforced weakly in both space and time. Several numerical examples involving transient radiation are presented to illustrate the high-order accuracy and efficiency achieved by the new space-time finite element formulation for transient structural acoustics with non-reflecting boundaries.
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A galerkin least-squares finite element method for the two-dimensional Helmholtz Equation
International Journal for Numerical Methods in Engineering, 1995Co-Authors: Lonny L. Thompson, Peter M. PinskyAbstract:In this paper a Galerkin least-squares (GLS) finite element method, in which residuals in least-squares form are added to the standard Galerkin Variational Equation, is developed to solve the Helmholtz Equation in two dimensions. An important feature of GLS methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes. Previous work has accomplished this for the one-dimensional Helmholtz Equation using dispersion analysis. In this paper, the selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy. For any given direction of wave propagation, an optimal GLS mesh parameter is determined using two-dimensional Fourier analysis. In general problems, the direction of wave propagation will not be known a priori. In this case, an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements. The optimal GLS parameters are derived for both consistent and lumped mass approximations. Several numerical examples are given and the results compared with those obtained from the Galerkin method. The extension of GLS to higher-order quadratic interpolations is also presented.
K C Le - One of the best experts on this subject based on the ideXlab platform.
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thermodynamic dislocation theory for non uniform plastic deformations
Journal of The Mechanics and Physics of Solids, 2018Co-Authors: K C LeAbstract:The present paper extends the thermodynamic dislocation theory developed by Langer, Bouchbinder, and Lookman to non-uniform plastic deformations. The free energy density as well as the positive definite dissipation function are proposed. The governing Equations are derived from the Variational Equation. As illustration, the problem of plane strain constrained shear of single crystal deforming in single slip is solved within the proposed theory.
Lonny L. Thompson - One of the best experts on this subject based on the ideXlab platform.
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a space time finite element method for structural acoustics in infinite domains part 2 exact time dependent non reflecting boundary conditions
Computer Methods in Applied Mechanics and Engineering, 1996Co-Authors: Lonny L. Thompson, Peter M. PinskyAbstract:Abstract In Part 1, a new space-time finite element method for transient structural acoustics in exterior domains was given. The formulation employs a finite computational fluid domain surrounding the structure and incorporates local time-dependent non-reflecting boundary conditions on the fluid truncation boundary. In this paper, new exact time-dependent non-reflecting boundary conditions are developed for solutions of the scalar wave Equation in three space dimensions. These high-order accurate absorbing boundary conditions are based on the exact impedance relation for the acoustic fluid through the Dirichlet-to-Neumann (DtN) map in the frequency domain and are exact for solutions consisting of the first N spherical wave harmonics. Time-dependent boundary conditions are obtained through an inverse Fourier transform procedure. Two alternative sequences of boundary conditions are derived; the first involves both temporal and spatial derivatives (local in time and local in space version), and the second involves temporal derivatives and a spatial integral (local in time and non-local in space version). These non-reflecting boundary conditions are incorporated as ‘natural’ boundary conditions in the space-time Variational Equation, i.e. they are enforced weakly in both space and time. Several numerical examples involving transient radiation are presented to illustrate the high-order accuracy and efficiency achieved by the new space-time finite element formulation for transient structural acoustics with non-reflecting boundaries.
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A galerkin least-squares finite element method for the two-dimensional Helmholtz Equation
International Journal for Numerical Methods in Engineering, 1995Co-Authors: Lonny L. Thompson, Peter M. PinskyAbstract:In this paper a Galerkin least-squares (GLS) finite element method, in which residuals in least-squares form are added to the standard Galerkin Variational Equation, is developed to solve the Helmholtz Equation in two dimensions. An important feature of GLS methods is the introduction of a local mesh parameter that may be designed to provide accurate solutions with relatively coarse meshes. Previous work has accomplished this for the one-dimensional Helmholtz Equation using dispersion analysis. In this paper, the selection of the GLS mesh parameter for two dimensions is considered, and leads to elements that exhibit improved phase accuracy. For any given direction of wave propagation, an optimal GLS mesh parameter is determined using two-dimensional Fourier analysis. In general problems, the direction of wave propagation will not be known a priori. In this case, an optimal GLS parameter is found which reduces phase error for all possible wave vector orientations over elements. The optimal GLS parameters are derived for both consistent and lumped mass approximations. Several numerical examples are given and the results compared with those obtained from the Galerkin method. The extension of GLS to higher-order quadratic interpolations is also presented.
Seonho Cho - One of the best experts on this subject based on the ideXlab platform.
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adjoint shape design sensitivity analysis of fluid solid interactions using concurrent mesh velocity in ale formulation
Finite Elements in Analysis and Design, 2014Co-Authors: Hong-lae Jang, Seonho ChoAbstract:Abstract A coupled Variational Equation for fluid–solid interaction (FSI) problems is derived using a steady state Navier–Stokes Equation for incompressible flows, an equilibrium Equation for geometrically nonlinear solids, a traction continuity condition at interfaces, and a pseudo-equilibrium Equation for mesh velocity. The moving boundary in arbitrary Lagrangian–Eulerian (ALE) formulation is included in the Variational Equations by the mesh velocity obtained from a displacement-loaded pseudo-structural problem at a concurrent configuration, which eventually facilitates to derive shape design sensitivity. A continuum-based adjoint shape sensitivity is derived under ALE formulation, which turns out to be very accurate and efficient due to the utilization of converged tangent and the linearity of both adjoint and sensitivity Equations. Through numerical examples, the obtained sensitivity is verified in terms of accuracy and efficiency compared with finite difference sensitivity and further applied to the shape optimization problem of finding a stiff structure while satisfying a volume constraint.
