Hyperbolic heat-conduction problems: Numerical simulations via explicit lax-wendroff-based finite element formulations

Kumar K. Tamma, Raju R. Namburu

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The paper describes numerical simulations for hyperbolic heat-conduction problems involving non-Fourier effects via explicit self-starting Lax-Weiidroff-based finite element formulations. For cases involving extremely short transient durations or for very low temperatures near absolute zero, the classical Fourier diffusion model for heat conduction breaks down since the wave nature of thermal energy transport becomes dominant. Major difficulties in numerical simulations include severe oscillatory solution behavior in the vicinity of the propagating shocks. The present paper describes an alternate methodology and different computational perspectives for effective modeling/analysis of hyperbolic heat-conduction models involving non-Fourier effects. In conjunction with the proposed formulations, smoothing techniques are incorporated to stabilize the oscillatory solution behavior and to accurately predict the propagating thermal disturbances. The capability of exactly capturing the propagating thermal disturbances at characteristic time-step values is noteworthy. Numerical test cases are presented to validate the proposed concepts for hyperbolic heat-conduction problems.

Original languageEnglish (US)
Pages (from-to)232-239
Number of pages8
JournalJournal of thermophysics and heat transfer
Issue number2
StatePublished - Apr 1991

Bibliographical note

Funding Information:
This research is supported in part by the NASA Langley Research Center, Hampton, Virginia, and the Flight Dynam- ics Laboratory, Wright Patterson Air Force Base, Ohio under Grant NAG-1-808. Partial support from a grant by the Uni- versity of Minnesota Graduate School and the Minnesota Supercomputer Institute is also acknowledged. Acknowledg-ment is also due to support, in part, by the Army High Performance Computing Research Center (AHPCRC), Min-neapolis, Minnesota.


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