Automated Symbolic Upscaling: 2. Model Generation for Extended Applicability Regimes

In this second part of the two paper series, we detail an algorithmic procedure for systematically implementing the generalized closure form strategy presented in Part 1. This strategy extends the applicability of homogenized models with respect to classical homogenization theory, as demonstrated in Part 1 where upscaled models are rigorously derived in moderately reactive physical regimes. After encoding the algorithm into Symbolica, an automated upscaling framework, we upscale two reactive mass transport problems and numerically validate the resulting nonlinear homogenized models by showing the absolute error estimates predicted by homogenization theory are satisfied. In both problems, nontrivial closure forms and closure problems are automatically formulated using the encoded strategy with no human interaction, nor prior knowledge regarding the closure required for the systems. We hope these demonstrations spark further interest in automated analytical frameworks for multiscale modeling, as such capabilities are invaluable for generating rigorous multiscale models of complex phenomena in porous media.

Automated summary

In this second part, an algorithmic procedure is presented for implementing the generalized closure form strategy described in Part 1. The algorithm is encoded into Symbolica, an automated upscaling framework, and is used to upscale two reactive mass transport problems. The resulting nonlinear homogenized models are numerically validated, and it is shown that the predicted absolute error estimates are satisfied. The automated strategy formulates closure forms and problems without human interaction or prior knowledge, demonstrating the value of automated analytical frameworks for multiscale modeling.