A delayed remap technique in multi-material ALE methods
Keywords:
mutli-material ALE formulation, delayed mesh relaxation, shock capture, adapted mesh refinementAbstract
A new mesh refinement method for multi-material ALE formulations is presented. The computational timestep of this approach is divided in 2 steps: a so-called Lagrangian step, during which the mesh deforms with the update of the solution, and a so-called Eulerian step, during which the mesh is remapped in order to preserve the mesh regularity and refine in the vicinity of the shock front. As test case the method is applied to the propagation of an explosive airblast, for which experimental results are available.
Downloads
References
Aquelet N., Seddon C., Souli M., Moatamedi M., “Initialisation of volume fraction in
fluid/structure interaction problem”, IJCrash, Vol. 10, No. 2, 2005.
Belytschko T., Liu W.K., Moran B., Nonlinear Finite Elements for Continua and Structures,
John Wiley & Sons, LTD, 2001.
Belytscko T., Flanagan D. F., Kennedy J. M., “Finite element method with user-controlled
meshes for fluid-structure interactions”, Comput. Methods Appl. Mech. Engrg., Vol. 33,
, p. 682-723.
Benson D.J., “Computational methods in Lagrangian and Eulerian Hydrocodes”, Comput.
Methods in Appl. Mech. Engrg., Vol. 72, 1992, p. 235-294.
Boyd S.D., Acceleration of a Plate Subject to Explosive Blast Loading - Trial Results,
Maritime Platforms Division Aeronautical and Maritime Research Laboratory, DSTOTN-
, 2000.
Brooks A. N., Hughes T. J. R., “Streamline upwind/Petrov-Galerkin formulations for
convection-dominated flows with particular emphasis on the incompressible Navier-
Stokes equations”, Comput. Methods in Appl. Mech. Engrg., Vol. 32, 1982, p. 199-259.
Donea J., “Arbitrary Lagrangian-Eulerian finite element methods”, Comput. Methods for
Transient Analysis (A84-29160 12-64), 1983, p. 473-516.
Hughes T. J. R., Liu W. K. and Zimmerman T. K., “Lagrangian-Eulerian finite element
formulation for viscous flows”, Comput. Methods Appl. Mech. Engrg., Vol. 21, 1981,
p. 329-349.
Hughes T. J. R., Mallet M., Mizukami A., “A new finite element formulation for
computational fluid dynamics: II. Beyond SUPG”, Comput. Methods Appl. Mech. Engrg.,
Vol. 54, 1986, p. 341-355.
Liu W. K., Chang H., Chen J.-S. and Belytschko T., “Arbitrary Lagrangian-Eulerian Petrov-
Galerkin finite elements for non-linear continua”, Comput. Methods in Appl. Mech.
Engrg., Vol. 68, 1988, p. 259-310.
Mallet M., A finite element method for computational fluid dynamics, Ph. D. Thesis, Stanford
University, Stanford, CA, 1985.
Souli M., Ouahsine A., Lewin L., “ALE and Fluid-Structure Interaction problems”, Comp.
Meth. Appl. Mech. Engrg., Vol. 190, 2000, p. 659-675.
Van Leer B., “Towards the Ultimate Conservative Difference Scheme, IV. A New Approach
to Numerical Convection”, Journal Computational Physics, Vol. 167, 1977, p. 276-299.
Wilkins M., “Calculation of elastic-plastic flow”, Methods in Computational Physics, Vol. 3,
Fundamental Methods in Hydrodynamics, (Academics Press, New York, 1964), p. 211-263.
Winslow A.M., “Numerical Solution of the Quasilinear Poisson Equation in a Nonuniform
Triangle Mesh”, J.Comput. Phys., Vol. 2, 1967, p. 149-172.
Young D.L., “Time-dependent multi-material flow with large fluid distortion”, Numerical
Methods for Fluids Dynamics, Ed. K. W. Morton and M.J. Baines, Academic Press, New-
York, 1982.
