Related papers: Numerical solution of shock and ramp compression f…
We study statistical properties of an NP-complete problem, the subset sum, using the methods and concepts of statistical mechanics. The problem is a generalization of the number partitioning problem, which is also an NP-complete problem and…
This paper represents a sequel to the previous one, where numerical solution of a quasistatic contact problem is considered for an elastic body in frictional contact with a moving foundation. The model takes into account wear of the contact…
Explicit numerical finite difference schemes for partial differential equations are well known to be easy to implement but they are particularly problematic for solving equations whose solutions admit shocks, blowups and discontinuities.…
We develop efficient and accurate numerical methods to solve a class of shallow shell problems of the von Karman type. The governing equations form a fourth-order coupled system of nonlinear biharnomic equations for the transverse…
Lightweight, single-use explosion containment structures provide an effective solution for neutralizing rogue explosives, combining affordability with ease of transport. This paper introduces a three-stage simulation framework that captures…
This paper identifies a new pathology that can be found for numerical simulations of nonlinear conservation law systems. Many of the difficulties already identified in the literature (rarefaction shocks, carbuncle phenomena, slowly moving…
We propose a numerical methodology for the simultaneous numerical simulation of four states of matter; gas, liquid, elastoplastic solids and plasma. The distinct, interacting physical processes are described by a combination of…
We propose a one-dimensional, nonconvex elastic constitutive model with higher gradients that can predict spontaneous fracture at a critical load via a bifurcation analysis. It overcomes the problem of discontinuous deformations without…
We consider the structure of mildly relativistic shocks in dense media, taking into account the radiation and pair loading, and diffusive radiation energy transfer within the flow. For increasing shock velocity (increasing post-shock…
The coupling of Reynolds and Rayleigh-Plesset equations has been used in several works to simulate lubricated devices considering cavitation. The numerical strategies proposed so far are variants of a staggered strategy where Reynolds…
Numerical simulation of compressible fluid flows is performed using the Euler equations. They include the scalar advection equation for the density, the vector advection equation for the velocity and a given pressure dependence on the…
Shock jump conditions are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly…
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work…
We present a numerical method for approximating the solutions of degenerate parabolic equations with a formal gradient flow structure. The numerical method we propose preserves at the discrete level the formal gradient flow structure,…
The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…
A new gradient-based formulation for predicting fracture in elastic-plastic solids is presented. Damage is captured by means of a phase field model that considers both the elastic and plastic works as driving forces for fracture. Material…
Crack micro-geometries and tribological properties pose an important impact on the elastic characteristics of fractured rocks. Numerical simulation as a promising way for this issue still faces some challenges. With the rapid development of…
This review is concerned with a discussion of numerical methods for the solution of the equations of special relativistic hydrodynamics (SRHD). Particular emphasis is put on a comprehensive review of the application of high-resolution…
Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov…
Kinetic equations are analyzed for thermal degradation of polymers. The governing relations are based on the fragmentation-annihilation concept. Explicit solutions to these equations are derived in two particular cases of interest. For…