Jordan–Cattaneo waves: Analogues of compressible flow

Abstract

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High-order fluxes in heat transfer with phonons and electrons: application towavepropagation

“…To do this, from a mathematical point of view, here we model a temperature wave as a planar surface S(t), propagating along the system with velocity V (unknown a priori), across which the time and/or the spatial derivatives of the state-space variables suffer jumps (i.e. at most finite discontinuities), whereas those field variables are continuous everywhere [44][45][46][47]. We refer readers to appendix A for some deeper comments about planar surfaces, as well as the relations used in the calculations below.…”

On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases

“…This extension of KSS methods to the nonlinear case can be accomplished through their combination with exponential propagation iterative (EPI) methods (see Ref. [25]), as has been accomplished for other PDEs (see Ref. [5]).…”

“…While the present manuscript was under review, Straughan [25, §7] published a generalization of the DJM that includes the effects of fluid thermal conductivity. A key feature of this formulation is that both the mechanical (i.e., acoustic) and thermal fields satisfy the requirements of causality, the causal nature of the latter stemming from Straughan's use of the Cattaneo‐Christov relation (rather than Fourier's law) to describe the heat flux vector.…”