Finite element/finite volume approaches with adaptive time stepping strategies for transient thermal problems

Transient thermal analysis of engineering materials and structures by space discretization techniques such as the finite element method (FEM) or finite volume method (FVM) lead to a system of parabolic ordinary differential equations in time. These semidiscrete equations are traditionally solved using the generalized trapezoidal family of time integration algorithms which uses a constant single time step. This single time step is normally selected based on the stability and accuracy criteria of the time integration method employed. For long duration transient analysis and/or when severe time step restrictions as in nonlinear problems prohibit the use of taking a larger time step, a single time stepping strategy for the thermal analysis may not be optimal during the entire temporal analysis. As a consequence, an adaptive time stepping strategy which computes the time step based on the local truncation error with a good global error control may be used to obtain optimal time steps for use during the entire analysis. Such an adaptive time stepping approach is described here. Also proposed is an approach for employing combinedFEM/FVM mesh partitionings to achieve numerically improved physical representations. Adaptive time stepping is employed thoughout to practical linear/nonlinear transient engineering problems for studying their effectiveness in finite element and finite volume thermal analysis simulations. Additional support and computing times were furnished by Minnesota Supercomputer Institute at the University of Minnesota.