We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity, and “architectural” includes both software and hardware environments. Many diverse multiphysics applications can be reduced, en route to their computational simulation, to a common algebraic coupling paradigm. Mathematical analysis of multiphysics coupling in this form is not always practical for realistic applications, but model problems representative of applications discussed herein can provide insight. A variety of software frameworks for multiphysics applications have been constructed and refined within disciplinary communities and executed on leading-edge computer systems. We examine several of these, expose some commonalities among them, and attempt to extrapolate best practices to future systems. From our study, we summarize challenges and forecast opportunities.

Laboratory experiments, pore‐scale simulations, and continuum (Darcy) ‐scale simulations were used to study mixing‐induced precipitation in porous media. In the experimental investigation, solutions containing Na₂CO₃ and CaCl₂ were each injected in different halves of a quasi two‐dimensional flow cell filled with quartz sand. As a result of the in situ mixing between the two solutions, a narrow calcite precipitate layer (less than 5 mm wide) of more or less uniform width was formed between the individual solutions. Pore‐scale simulations were conducted to help understand the mechanism of precipitation layer formation. The effect of the Peclet number, Pe, and the Damköhler number, Da, on mixing induced precipitation was also investigated. Pore‐scale simulations revealed the presence of large pore‐scale concentration gradients. This, and the presence of features, such as the precipitation layer, with characteristic lengths on the order of the average sand grain diameter, indicate the absence of a clear scale separation required for the strict derivation of Darcy‐scale advection‐dispersion equations. Nevertheless, we found that an adaptive high‐resolution model based on advection‐dispersion equations with grid sizes in the mixing zone smaller than the size of the sand grains can qualitatively reproduce the essential features of the experiment. As an alternative to computationally expensive high‐resolution simulations, we proposed new forms for the homogeneous and heterogeneous reaction terms in Darcy‐scale advection dispersion equations. These terms involve transport and mixing indices that account for highly nonuniform pore‐scale concentration distributions and highly localized reactions. The proposed model accurately estimates the changes in solute concentrations due to homogenous and heterogeneous reactions during precipitation of minerals, observed in the pore‐scale simulations, while conventional low‐resolution advective‐dispersion equations produced erroneous results.