Using Isogeometric Analysis to Model Cylindrical Shock Hydrodynamics
Abstract Not Provided
Mathematics & Computing(97)↗
Engineering topics
Shashkov, Mikhail J.
Publications and source records attributed to Shashkov, Mikhail J..
An intersection based ALE scheme (xALE) for cell centered hydrodynamics (CCH)
Abstract Not Provided
hydrodynamics, cell-centered, ALE, synchronized FC↗
Support Operators Method for the Diffusion Equation in Multiple Materials
A second-order finite difference scheme for the solution of the diffusion equation on non-uniform meshes is implemented. The method allows the heat conductivity to be discontinuous. The algorithm is formulated on a one dimensional mesh and is derived using the support operators method. A key component of the derivation is that the discrete analog of the flux operator is constructed to be the negative adjoint of the discrete divergence, in an inner product that is a discrete analog of the continuum inner product. The resultant discrete operators in the fully discretized diffusion equation are symmetric and positive definite. The algorithm is generalized to operate on meshes with cells which have mixed material properties. A mechanism to recover intermediate temperature values in mixed cells using a limited linear reconstruction is introduced. The implementation of the algorithm is verified and the linear reconstruction mechanism is compared to previous results for obtaining new material temperatures.
97 MATHEMATICS AND COMPUTING↗
Surrogate Guderley Test Problem Definition
The surrogate Guderley problem (SGP) is a 'spherical shock tube' (or 'spherical driven implosion') designed to ease the notoriously subtle initialization of the true Guderley problem, while still maintaining a high degree of fidelity. In this problem (similar to the Guderley problem), an infinitely strong shock wave forms and converges in one-dimensional (1D) cylindrical or spherical symmetry through a polytropic gas with arbitrary adiabatic index γ, uniform density ρ 0 , zero velocity, and negligible pre-shock pressure and specific internal energy (SIE). This shock proceeds to focus on the point or axis of symmetry at r = 0 (resulting in ostensibly infinite pressure, velocity, etc.) and reflect back out into the incoming perturbed gas.
97 MATHEMATICS AND COMPUTING↗
Simulation and Analysis of Converging Shock Wave Test Problems
Results and analysis pertaining to the simulation of the Guderley converging shock wave test problem (and associated code verification hydrodynamics test problems involving converging shock waves) in the LANL ASC radiation-hydrodynamics code xRAGE are presented. One-dimensional (1D) spherical and two-dimensional (2D) axi-symmetric geometric setups are utilized and evaluated in this study, as is an instantiation of the xRAGE adaptive mesh refinement capability. For the 2D simulations, a 'Surrogate Guderley' test problem is developed and used to obviate subtleties inherent to the true Guderley solution's initialization on a square grid, while still maintaining a high degree of fidelity to the original problem, and minimally straining the general credibility of associated analysis and conclusions.
97 MATHEMATICS AND COMPUTING↗