ARES: An efficient approach to adaptive time integration for stiff Differential-Algebraic Equations
Résumé
In the broad context of solving systems of stiet64256; Diet64256;erential-Algebraic Equa-tions (DAE), in-between a basic Euler implicit scheme with a et64257;xed timestepand adaptive timestep and higher order approaches, we propose the Adap-tive Relaxed Euler Scheme (ARES) an implicit Euler scheme with an adaptivetimestep, in conjunction with a nonlinear solver using the Newton method.We stick to a 1st-order time scheme and the adaptive quality uses very fewadditional operations and is therefore much less costly and easier to imple-ment, while remaining adaptive to the local stiet64256;ness of the system. The overallprinciple of ARES allowing to reduce accuracy of a transient calculation inorder to get faster to a steady state, proves to be especially relevant in thecontext of complex industrial reactive transport simulations, where only thesteady state of the plant is of interest, while eluding often evaluation througha direct calculation. In cases where computational time is of the essence, ourapproach is demonstrated through practical examples to oet64256;er a simple andvalid way to obtain steady-state solutions reliably and fast.