Analysis of Dynamic Problems in Fully Saturated Porous Media Using an Embedded Velocity Integration Formulation With an Adaptive Runge–Kutta Method

ABSTRACT This contribution presents a dynamic binary Theory of Porous Media (TPM) model using an embedded velocity integration (EVI) formulation. The inclusion of dynamic effects into a TPM model leads to an increase in the number of unknown quantities and may also limit the choice of fitting time integration methods. By switching to a velocity formulation the amount of unknown quantities is kept to a minimum and the necessity of a time integration scheme being able to produce a second material time derivative is avoided. The used EVI formulation was verified and its advantage concerning computational time was shown by a comparison to a classic approach by Diebels and Ehlers. Both approaches were simulated with an adaptive, embedded, stiffly accurate, explicit, singly, diagonally implicit Runge–Kutta (saESDIRK) time integration method to decrease the computational time even more.