Abstract
A modification of the wave-propagation algorithm is used as a tool for determining contact quantities in a finite-volume scheme for the numerical simulation of two-dimensional thermoelastic wave propagation in inhomogeneous media. The modification is needed to provide the satisfaction of the thermodynamic consistency conditions between adjacent elements. It appears that the algorithm is thermodynamically consistent except for the limiter functions. Therefore, a composite scheme is used where the Godunov step is applied after each three second-order Lax–Wendroff steps. Elimination of source terms is made following the method of balancing source terms after independent solution of the heat conduction equation.
Highlights
The question of conceiving an accurate numerical scheme for thermoelasticity was raised recently in conjunction with the problem of the simulation of the progress of phase-transition fronts in crystalline substances. The latter is a free boundary problem which involves rapid localized changes in the field solution. It is with this problem in mind that the authors have developed a numerical scheme dealing first with the case of materially inhomogeneous thermoelastic conductors with smooth or abrupt property variations but no phase changes
That the recently proposed composite schemes [3] are more convenient for our purposes, because of the use of filters that are consistent with differential equations
The construction of the wave propagation algorithm begins with establishing the firstorder Godunov scheme in terms of these fluctuations [1]: qikj+1 = qikj −
Summary
The question of conceiving an accurate numerical scheme for thermoelasticity was raised recently in conjunction with the problem of the simulation of the progress of phase-transition fronts in crystalline substances. The latter is a free boundary problem which involves rapid localized changes in the field solution. Certain assumptions about the smoothness of solution are typically used to approximate derivatives in standard finite-difference methods These approximations are not valid near discontinuities in the material parameters. The thermodynamic consistency conditions are extremely important for the modeling of phase transitions in solids It seems, that the recently proposed composite schemes [3] are more convenient for our purposes, because of the use of filters that are consistent with differential equations. Results of computation for certain test problems show the efficiency and physical consistency of the algorithm
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
