Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion 23.3.2006 ISCM-20 Copyright by PZ Bar-Yoseph ©

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Presentation transcript:

Pinhas Z. Bar-Yoseph Computational Mechanics Lab. Mechanical Engineering, Technion ISCM-20 Copyright by PZ Bar-Yoseph ©

Bar-Yoseph, Appl. Num. Math. 33, , 2000

DSM for Dynamic systems Aharoni & Bar-Yoseph, Comp. Mech. 9, , 1992

Discontinuous element

Plat & Bar-Yoseph, 27 th Israel Conf. Mech. Eng , 1998 Nonlinear Spatio-Temporal Dynamics of a Flexible Rod

Bar-Yoseph, Appl. Num. Math. 33, , 2000

Nave, Bar-Yoseph & Halevi, Dynamics. & Control. 9, , 1999 The unicycle system, presents an example of inherently unstable system which can be autonomously controlled and stabilized by a skilled rider -required to maintain the unicylce’s upright position -required to maintain lateral stability -the friction torque is assumed to be dependent on the yew rate only

The adaptive technique performed very well for all stiff systems that we have experienced with (convection, radiation and chemical reactions), and is competitive with the best Gear-type routines

Space-Time Discontinuous Approximations

Bar-Yoseph & Elata, IJNME, 29, , 1990

Bar-Yoseph & Elata & Israeli, IJNME, 36, , 1993; Golzman & Bar-Yoseph (Project)

Bar-Yoseph & Elata & Israeli, IJNME, 36, , 1993; Golzman & Bar-Yoseph (Project)

Bar-Yoseph & Elata, IJNME, 29, , 1990

Fischer & Bar-Yoseph, IJNME, 48, , 2000

Adaptive Level of Details Technique for Meshing Advanced CAD Visualization Methods

Morphing between Meshes at Different Times

DGM Elements are discontinuous. CGM Conforming elements.

Space-Time Discontinuous Approximations

Gauss-Lobatto nodes are clustered near element boundaries and are chosen because of their interpolation and quadrature properties. Mass lumping by nodal quadrature. Exponential rate of convergence. The increase in the due to the discontinuity at the interelement boundaries is balanced in high order elements. Discontinuous SPECTRAL ELEMENTS

Flux Splitting Bar-Yoseph,Comput. Mech., 5, , 1989

Nonlinear Wave Eq. Miles Rubin (2005)

Flux splitting for non homogeneous

where: The effective wave speed: In a matrix form: Traper & Bar-Yoseph (Project)

The Jacobian matrix: The eigenvalues: The corresponding eigenvectors:

Displacement Traper & Bar-Yoseph (Project)

Velocity

Strain

-Time for breakdown [Lax (1964)]:

Velocity at t = 3 sec x bilinear biquadratic

Strain at t = 3 sec x bilinear biquadratic

Bar-Yoseph et al., JCP, 119, 62-74, 1995

Bar-Yoseph & Moses, IJNMHFF, 7, , 1997

Cockburn& Shu, JCP, 84, 90, 1989; Basi & Rebay, JCP, 131, , 1997