An efficient adaptive time-marching formulation for decoupled analysis of generalized thermo-mechanical models
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O R I G I NA L PA P E R
Delfim Soares Jr.
An efficient adaptive time-marching formulation for decoupled analysis of generalized thermo-mechanical models
Received: 22 May 2020 © Springer-Verlag GmbH Austria, part of Springer Nature 2020
Abstract In this paper, a locally-defined stabilized adaptive explicit approach is considered to analyse generalized coupled thermo-mechanical models. In this sense, a modified central difference method is applied, which performs adapting itself along the solution process, considering the properties and results of the model, as well as the relations between the adopted temporal and spatial discretizations. The proposed technique enables stabilized decoupled analyses, allowing each “phase” of the coupled model to be handled separately, without considering stability restrictions for their time solutions, providing a very versatile and efficient methodology. In addition, the new approach is designed as a single-solve framework based on reduced systems of equations, which further greatly improves the efficiency of the technique. The new method enables adaptive algorithmic dissipation in the higher modes, and it is highly accurate, simple to implement and entirely automated, requiring no decision or expertise from the user. Numerical results are presented at the end of the manuscript, illustrating the performance and effectiveness of the new approach.
1 Introduction A novel time-marching solution technique is proposed here to analyse generalized thermo-mechanical coupled models. The main difference between classical and generalized thermo-mechanical formulations is that the latter takes into account the wave nature of thermal transfer. In the classical thermo-mechanical formulation, the equation of motion is of wave type, while the heat-conduction equation is of diffusion type, which implies that thermal disturbances propagate with infinite velocity. To overcome this unrealistic feature, in the generalized thermo-mechanical formulation [1–3], both governing equations of the model are of wave type, providing a plausible physical explanation for the behaviour of heat transfer in models where the standard Fourier conduction law does not properly apply. The idea here is to apply locally stabilized explicit procedures [4,5] to analyse each “phase” of the generalized coupled model and, consequently, allow the governing equations of the problem to become decoupled by the time solution procedure, enabling more efficient computations. In general, time marching procedures can be subdivided into explicit and implicit formulations. In an explicit approach, all constitutive variables are available from computations at previous time steps, and, in combination with diagonal matrices, these methods do not require the solution of any system of equations. In an implicit approach, on the other hand, the constitutive variables are expressed as functions of the current time of analysis. In this case, solver routines are necessary, and, when coupled models are regarded, much larger (bad-conditioned) syste
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