Nonlinear porodynamic analysis by adaptive semi-explicit/explicit time marching formulations

Abstract

In this paper, we propose two adaptive semi-explicit/explicit numerical approaches to analyse nonlinear porodynamic models. In this context, simple, stabilised, non-iterative, reduced effort, decoupled formulations are developed, in which the time integrators of the time marching procedures are locally defined, allowing distinct values to be assigned to each element of the spatial discretisation. Thus, linked formulations between the adopted temporal and spatial solution procedures take place, allowing the time marching techniques to adapt to the properties of the discretised model properly and locally. For each technique, each phase of the coupled problem is treated separately, uncoupling the governing equations of the porous model. Therefore, simpler, smaller and better-conditioned systems of equations are obtained, which can be handled without considering any iterative computation, even when nonlinear models are regarded. Additionally, reduced systems of equations may arise for each phase of the model, which may then be analysed without considering stability restrictions for their time solutions. Also, incompressible and impermeable media may be directly analysed, without requiring any special discretisation procedure, as is the case in standard solution techniques. At the end of the manuscript, numerical examples are presented, illustrating the effectiveness of the proposed new formulations.