The piecewise parabolic method for elastic-plastic flow in solids.

A numerical technique of high-order piecewise parabolic method in combination of HLLD ("D" denotes Discontinuities) Riemann solver is developed for the numerical simulation of elastic-plastic flow. The introduction of the plastic effect is realized by decomposing the total deformation gradient tensor as the product of elastic and plastic deformation gradient tensors and adding plastic source term to the conservation law model equation with the variable of the elastic deformation gradient tensor. For the solution of the resulting inhomogeneous equation system, a temporal splitting strategy is adopted and a semi-implicit scheme is performed to solve the ODES in the plastic step, which is conducted to account for the contributions from plastic source terms. As seen from the results of test cases involving large deformation and high strain rate, the computational model used can reflect the characteristics of constitutive relation of material under strong impact action and our numerical method can realize the exact simulation of the elastic-plastic behavior of solid material, especially the accurate capture of the elastic-plastic waves. Further, it could also deal with high-speed impact problems with multi-material components, catching material interfaces correctly and keeping the interfaces sharp, when combined with interface tracking technique such as the level-set algorithm.

The piecewise parabolic method for Riemann problems in nonlinear elasticity.

We present the application of Harten-Lax-van Leer (HLL)-type solvers on Riemann problems in nonlinear elasticity which undergoes high-load conditions. In particular, the HLLD ("D" denotes Discontinuities) Riemann solver is proved to have better robustness and efficiency for resolving complex nonlinear wave structures compared with the HLL and HLLC ("C" denotes Contact) solvers, especially in the shock-tube problem including more than five waves. Also, Godunov finite volume scheme is extended to higher order of accuracy by means of piecewise parabolic method (PPM), which could be used with HLL-type solvers and employed to construct the fluxes. Moreover, in the case of multi material components, level set algorithm is applied to track the interface between different materials, while the interaction of interfaces is realized through HLLD Riemann solver combined with modified ghost method. As seen from the results of both the solid/solid "stick" problem with the same material at the two sides of contact interface and the solid/solid "slip" problem with different materials at the two sides, this scheme composed of HLLD solver, PPM and level set algorithm can capture the material interface effectively and suppress spurious oscillations therein significantly.

Numerical study of initial perturbation effects on Richtmyer-Meshkov instability in nonuniform flows.

The effects of an initial perturbation on Richtmyer-Meshkov instability are numerically studied by simulating the process of incident shock (Ma=1.27) impacting different groups of initial multimode cosine interfaces formed by different amplitudes in initially nonuniform flows whose density is a Gaussian function. The numerical results indicate that the evolution of the interface with a large initial amplitude in a low-density nonuniform area grows fastest, while that with a small initial amplitude in a high-density nonuniform area grows slowly. Further analysis of vorticity and circulation illustrates these phenomena. The interface with a large initial amplitude in a low-density zone possesses a larger density gradient, which results in a larger amount of vorticity and circulation, leading to the fast-changing evolution of the interface. Distinctive evolution mechanisms of Richtmyer-Meshkov instability between the nonuniform flows and the uniform flows are analyzed in detail.

Numerical simulation of the Richtmyer-Meshkov instability in initially nonuniform flows and mixing with reshock.

Based on previous instability experiments of the double mode perturbed interface in initially nonuniform flows, we numerically investigate the effect of the nonuniformity of flows on the evolution of instability in a nonlinear regime after reshock by adopting two different nonuniform coefficients (δ_{1} = 0.6162 and δ_{2} = 0.4961) in the Gaussian distribution of the initial nonuniform density. We obtain the evolution of the mixing zone width and vortex structure of the air-SF_{6} interface and compare the circulation discrepancies of the nonuniform and uniform flows before and after reshock. These results indicate that the nonuniformity of the initial flow has great effect on the evolution of instability in the linear regime and the weak nonlinear regime prior to reshock. However, the mixing layer has little dependence on the nonuniformity of the initial flow in the nonlinear regime after reshock; namely, the effect of the nonuniformity is reduced significantly as the instability enters the strongly nonlinear regime after reshock. Although the growth rate of the perturbations has a significant increase, the characteristics of the flow like the mixing width, vorticity, and circulation are close to those of a uniform flow.

Investigation of the Richtmyer-Meshkov instability with double perturbation interface in nonuniform flows.

A nonuniform SF6 gas flow initial condition has been actualized in the context of shock tube experiment for the Richtmyer-Meshkov instability study. Two kinds of amplitude have been used to design the membrane supports which initially materialize the gaseous interface. The visualizations of air/SF6 sinusoidal interfaces and shock wave propagations in the nonuniform field were obtained by Schlieren photography. Experiments are in very good agreement with simulations for the air/SF6 case, but due to the initial nonuniform effects, Sadot model and Zhang-Sohn theory are far beyond the experimental and calculation results.

Experimental and numerical study of shock-accelerated elliptic heavy gas cylinders.

We studied the evolution of elliptic heavy SF6 gas cylinder surrounded by air when accelerated by a planar Mach 1.25 shock. A multiple dynamics imaging technology has been used to obtain one image of the experimental initial conditions and five images of the time evolution of elliptic cylinder. We compared the width and height of the circular and two kinds of elliptic gas cylinders and analyzed the vortex strength of the elliptic ones. Simulations are in very good agreement with the experiments, but due to the different initial gas cylinder shapes, a certain difference of the initial density peak and distribution exists between the circular and elliptic gas cylinders, and the latter initial state is more sensitive and more inenarrable.