We consider a simple 1D multi-material problem, which captures key aspects of inertial confinement fusion (ICF) implosion dynamics, on unstructured 2D and 3D meshes. The problem consists of two regions, each with an ideal gas equation of state. Initial conditions and material properties are specified according to the following diagram:
The outer surface drives a spherical shock wave inward. The interface between the high- and low-density materials should remain perfectly spherical for all time due to the spherical symmetry of the velocity drive. However, discretization errors of the initial geometry and subsequent error introduced by the numerical algorithm will be amplified over time since the interface is subject to both Richtmyer-Meshkov (RM) and Rayleigh-Taylor (RT) instabilities. Maintaining spherical symmetry on 2D and 3D unstructured meshes remains a major challenge for most Lagrangian (or ALE) schemes .
2D Axisymmetric Lagrangian Simulations with Q2-Q1 Finite Elements on Unstructured Meshes
Results for density and curvilinear mesh in the 2D axisymmetric ICF-like problem on a uniform unstructured mesh at times t = 0.0, 0.08 and 0.15.
3D Lagrangian Simulations with Q1-Q0, Q2-Q1 and Q4-Q3 Finite Elements on an Unstructured Mesh
Results for density and curvilinear mesh in the 3D ICF-like problem on an unstructured mesh using Q1-Q0, Q2-Q1 and Q4-Q3 finite elements (top to bottom) at times t = 0.0, 0.08 and 0.15. The three calculations have the same number of kinematic degrees of freedom.
2D Planar Perturbed ALE Simulations with Q4-Q3 Finite Elements on Unstructured Meshes
2D perturbed ICF simulation results on unstructured uniform grid High-order ALE methods excel at minimizing mesh imprinting on non-uniform and unstructured meshes.
Multi-material Cylindrical ALE Simulation
2D perturbed ICF simulation results on unstructured grid with two materials and second order finite element method at different time instances (click for larger view).