Application of the HughesLIU algorithm to the 2dimensional heat equation
Abstract
An implicit explicit algorithm for the solution of transient problems in structural dynamics is described. The method involved dividing the finite elements into implicit and explicit groups while automatically satisfying the conditions. This algorithm is applied to the solution of the linear, transient, two dimensional heat equation subject to an initial condition derived from the soluton of a steady state problem over an Lshaped region made up of a good conductor and an insulating material. Using the IIT/PRIME computer with virtual memory, a FORTRAN computer program code was developed to make accuracy, stability, and cost comparisons among the fully explicit Euler, the HughesLiu, and the fully implicit CrankNicholson algorithms. The HughesLiu claim that the explicit group governs the stability of the entire region while maintaining the unconditional stability of the implicit group is illustrated.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1982
 Bibcode:
 1982STIN...8310388M
 Keywords:

 Heat Transfer;
 Thermodynamics;
 Transient Response;
 Algorithms;
 Linear Equations;
 Thermal Conductivity;
 Thermal Stability;
 Fluid Mechanics and Heat Transfer