T.E. Tezduyar and M. Behr, Finite element solution strategies for large-scale flow simulations, Comput. Meth. Appl. Mech. Engrg. 112 (1994) 3--24.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in numerical simulation of free surface applications. Depending on the physical characteristic of the problem, either a moving mesh or fixed mesh technique is used. In the moving mesh technique, the nodal coordinates on the free surface are moved to track the motion of the free surface [3 6]. The space time finite element method is an example of the moving mesh technique [4,6] In the space time method, the finite element formulations are written over the space time domain. As a result, the motion of the free surface is taken into account automatically by simply moving the mesh. ....

....characteristic of the problem, either a moving mesh or fixed mesh technique is used. In the moving mesh technique, the nodal coordinates on the free surface are moved to track the motion of the free surface [3 6] The space time finite element method is an example of the moving mesh technique [4,6]. In the space time method, the finite element formulations are written over the space time domain. As a result, the motion of the free surface is taken into account automatically by simply moving the mesh. Here, the finite element functions are both linear in space and time, continuous in space, ....

[Article contains additional citation context not shown here]

M. Behr and T. Tezduyar, "Finite Element Solution Strategies for Large-Scale Flow Simulations," Computer Methods in Applied Mechanics and Engineering, 112 (1994), 3-24.

....BERGER, HALLBERG, HOWINGTON, KELLEY, SCHMIDT, STAGG, AND TOCCI FIG.3.1.3D Heterogeneous Column Clay Silt Sand X Y Z We discretized the equation on an unstructured tetrehedral mesh. We used the piecewise constant in time and piecewise linear in space finite element discretizations from [1]. The residual formulation of Richards equation is R ##;w#= R Q n R###w h dQ = R Qn # S S S ## # # h t # S## h # t # w h dQ , R Qn rw h : h K S k r # # h # r # # h z #i dQ , R# n # w h # n # # S S # # S # # h # # h # n ....

M. BEHR AND T. E . TEZDUYAR,Finite element solution strategies for large--scale flow simulations, Computer Methods in Applied Mechanics and Engineering, 112 (1994), pp. 3--24.

....8 JENKINS, BERGER, HALLBERG, HOWINGTON, KELLEY, SCHMIDT, STAGG, AND TOCCI FIG. 3.1. 3D Heterogeneous Column Clay Silt Sand X Y Z We discretized the equation on an unstructured tetrehedral mesh. We used the piecewise constant in time and piecewise linear in space finite element discretizations from [1]. The residual formulation of Richards equation is R ( w) R Qn R ( w h dQ = R Qn ae S S S ( h t j S( h ) t oe w h dQ Gamma R Qn rw h : h K S k r i h j r i h z ji dQ Gamma R Omega n i w h j n Delta ae S S i S i ....

M. BEHR AND T. E. TEZDUYAR, Finite element solution strategies for large--scale flow simulations, Computer Methods in Applied Mechanics and Engineering, 112 (1994), pp. 3--24.

.... Gamma = Gamma g [ Gamma h : In x 3 we give numerical results for a test case. These results show that our preconditioners have good scalability and that our coarse grid formulation is performing well. 2. NEWTON KRYLOV SCHWARZ The weak formulation of the Navier Stokes equations as given in [1] leads to implicit temporal integration. The discretization of the weak formulation leads to a system of nonlinear equations that must be solved at each time step. These equations are solved via Newton Krylov Schwarz (NKS) methods, which are described below. NKS methods [11] use a Krylov subspace ....

....riprap model results are being used to evaluate three dimensional models of the river bend. 4 The equations were discretized on unstructured tetrehedral meshes in three space dimensions. We used the piecewise constant in time and piecewise linear in space finite element discretizations from [1]. These discretizations are implicit in time and therefore a discretized nonlinear elliptic problem must be solved at each time step. The Galerkin least squares methods of [6] 8] 9] and [12] were used to stabilize the discretization. The meshes were generated using GMS [2] Initially a ....

M. Behr and T. E. Tezduyar. Finite element solution strategies for large--scale flow simulations. Computer Methods in Applied Mechanics and Engineering, 112:3--24, 1994.

.... Gamma = Gamma g [ Gamma h : In x 3 we give numerical results for a test case. These results show that our preconditioners have good scalability and that our coarse grid formulation is performing well. 2. NEWTON KRYLOV SCHWARZ The weak formulation of the Navier Stokes equations as given in [1] leads to implicit temporal integration. The discretization of the weak formulation leads to a system of nonlinear equations that must be solved at each time step. These equations are solved via Newton Krylov Schwarz (NKS) methods, which are described below. NKS methods [11] use a Krylov subspace ....

....These riprap model results are being used to evaluate three dimensional models of the river bend. The equations were discretized on unstructured tetrehedral meshes in three space dimensions. We used the piecewise constant in time and piecewise linear in space finite element discretizations from [1]. These discretizations are implicit in time and therefore 4 a discretized nonlinear elliptic problem must be solved at each time step. The Galerkin least squares methods of [6] 8] 9] and [12] were used to stabilize the discretization. The meshes were generated using GMS [2] Initially a ....

M. Behr and T. E. Tezduyar. Finite element solution strategies for large--scale flow simulations. Computer Methods in Applied Mechanics and Engineering, 112:3--24, 1994.

No context found.

M. Behr, T. Tezduyar, Finite element solution strategies for large-scale flow simulations, Computer Methods in Applied Mechanics and Engineering 112 (1994) 3--24.

No context found.

M. Behr and T.E. Tezduyar. Finite element solution strategies for large-scale flow simulations. Computer Methods in Applied Mechanics and Engineering, 112, 3--24, (1994). 10

....equations are written over the space time domain of the problem. Consequently, changes in the shapeofthe spatial domain due to the motion of the boundaries and interfaces are taken into account automatically. This approach has been successfully used to solvesloshing problems [4], flows past a surface piercing cylinder [5] as well as other classes of deforming domain problems [6, 7] In the context of free surface problems in complex geometries, the DSD SST formulation must be coupled with a suitable algorithm for the motion of the free surface, such as the elevation ....

....surface described by theboundary # t as t traverses I n .Asitisthecasewith# t ,surfaceP n is decomposed into (P n ) g and (P n ) h with respect to the type of boundary condition (Dirichlet and Neumann) being applied. After introducing suitable trial solution spaces for the velocity and pressure [4], S u ) n and (S p ) n , and test function spaces, V u ) n and (V p ) n ,thestabilized space time formulation of Equations (1) and (2)iswritten as follows: given (u ) n , find u u ) n and p p ) n such that u ) n and #q p ) n : #(u ....

[Article contains additional citation context not shown here]

M. Behr and T.E. Tezduyar, "Finite element solution strategies for large-scale flow simulations ", Computer Methods inApplied Mechanics and Engineering, 112 (1994) 3--24.

....#(u dQ Q e # CONT dQ = Pn ) h dP. 9) The following notation is being used inEquation(9) n = lim ##0 u(t n #) dQ= d#dt, Pn . dP = d#dt. 10) Thestabilization parameters # MOM and # CONT follow definitions given in [6]and[7] The DSD SST method, when applied on deforming domains, involves deformed space time elements, and automatically takes into account the moving frame of reference in which the nodal degrees of freedom (velocity, pressure) are computed. Therefore, the usual explicit ALE modifications to ....

M. Behr and T.E. Tezduyar, "Finite element solution strategies for large-scale flow simulations", Computer Methods in Applied Mechanics and Engineering, 112 (1994) 3-- 24.

....(1) 2) The fourth integral Computer Methods in Applied Mechanics and Engineering, 123 309 316 (1995) 5 enforces, weakly, the continuity of the velocity field in time. The two series of element level integrals in the formulation are the least squares stabilization terms. The reader can refer to [8 10] for further details regarding the space time formulation for incompressible flows, including definitions of the stabilization parameters. 3.2. Velocity Pressure Stress Formulation The velocity pressure stress formulation presented here is a restriction of the general formulation presented in ....

M. Behr and T.E. Tezduyar, "Finite element solution strategies for large-scale flow simulations", Computer Methods in Applied Mechanics and Engineering, 112 (1994) 3-- 24.

....is being used in Equation (15) u h ) n = lim ##0 u(t n #) 16) Z Qn . dQ= Z In Z# h t . d# dt, 17) Z Pn . dP = Z In Z # h t . d#dt. 18) Computational Mechanics, 23 (1999) 117 123 5 The definitions of the stabilization parameters # MOM and # CONT can be found in Behr and Tezduyar (1994). The solution to Equation (15) is obtained for all of the space time slabs Q 0 ,Q 1 , Q N 1 sequentially, and the computations start with (u h ) 0 = u h 0 . 19) The stabilized finite element formulation of Equation (7) can be written as Z S # h #H h #t u h s #H h ....

....to specify the motion of the mesh based on some pre defined rules. This approach can be employed only in cases where the changes in the shape of the spatial domain is su#ciently simple. An earlier example, parallel 3D computation of sloshing in a vertically vibrating container, can be found in Behr and Tezduyar (1994). In the 3D free surface flow problem presented in Section 8.2, we move the nodal points only in the vertical direction. Once the new location of the free surface is calculated, the nodes are redistributed along the vertical lines according to a geometric progression rule. By doing so, we place ....

Behr, M.; Tezduyar, T.E. 1994: Finite element solution strategies for large-scale flow simulations. Computer Methods in Applied Mechanics and Engineering, 112: 3--24.

No context found.

T.E. Tezduyar and M. Behr, Finite element solution strategies for large-scale flow simulations, Comput. Meth. Appl. Mech. Engrg. 112 (1994) 3--24.

No context found.

Behr, M., and Tezduyar, T. :"Finite Element Solution Strategies for Large-Scale Flow Simulations", Comp. Meth. Appl. Mech. Engng., (1994), 112, 3-24.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC