A non-oscillatory method for spallation studies

Abstract

SUMMARYThis paper introduces a non-oscillatory method, the finite element flux-corrected transport (FE-FCT) method for spallation studies. This method includes the implementation of a one-dimensional FCT algorithm into a total Lagrangian finite element method. Consequently, the FE-FCT method can efficiently eliminate fluctuations behind shock wave fronts without smearing them. In multidimensional simulations, the one-dimensional FCT algorithm is used on each grid line of the structured meshes to correct the corresponding component of nodal velocities separately. The requirement of structured meshes is satisfied by using an implicit function so that arbitrary boundaries of the simulated object can be described. In this paper, the proposed FE-FCT method is applied in spallation studies. Oneand two-dimensional examples show this non-oscillatory method could be one of the candidates to accurately predict spallation and the spall thickness.

Peridynamics with Corrected Boundary Conditions and Its Implementation in Multiscale Modeling of Rolling Contact Fatigue

“…It should be noted that the oscillations behind waves are due to numerical errors and could be corrected by the°ux-corrected algorithms. [82][83][84] Another approach to dramatically reducing the errors due to the boundary e®ect is using more material points, i.e.,¯ne meshes, as discussed in Sec. 3…”

Random neural networks for dimensionality reduction and regularized supervised learning

“…Generally, the oscillation occurs because numerical methods have difficulty reproducing strong discontinuities.A common solution is using artificial viscosity to smooth the shock wave fronts. In this Chapter, the flux-corrected transport (FCT) algorithm[151] is applied to eliminate the oscillations.Due to the hyperelastic nature of LJ potential when LJ bonds are compressed, the secant modulus is larger at a higher compressive stress, and the wave speed is faster. Consequently, the unloading wave front becomes gentler while the loading wave front remains steep.…”