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Finding a numerical method to model solute transport in porous media with high heterogeneity is crucial, especially when chemical reactions are involved. The phase space formulation termed the multi-advective water mixing approach (MAWMA) was proposed to address this issue. The water parcel method (WP) may be obtained by discretizing MAWMA in space, time, and velocity. WP needs two transition matrices of velocity to reproduce advection (Markovian in space) and mixing (Markovian in time), separately. The matrices express the transition probability of water instead of individual solute concentration. This entails a change in concept, since the entire transport phenomenon is defined by the water phase. Concentration is reduced to a chemical attribute. The water transition matrix is obtained and is demonstrated to be constant in time. Moreover, the WP method is compared with the classic random walk method (RW) in a high heterogeneous domain. Results show that the WP adequately reproduces advection and dispersion, but overestimates mixing because mixing is a sub-velocity phase process. The WP method must, therefore, be extended to take into account incomplete mixing within velocity classes.

Abstract The dynamics of isolated-photon plus two-jet production in pp collisions at a centre-of-mass energy of 13 TeV are studied with the ATLAS detector at the LHC using a dataset corresponding to an integrated luminosity of 36.1 fb−1. Cross sections are measured as functions of a variety of observables, including angular correlations and invariant masses of the objects in the final state, γ + jet + jet. Measurements are also performed in phase-space regions enriched in each of the two underlying physical mechanisms, namely direct and fragmentation processes. The measurements cover the range of photon (jet) transverse momenta from 150 GeV (100 GeV) to 2 TeV. The tree-level plus parton-shower predictions from Sherpa and Pythia as well as the next-to-leading-order QCD predictions from Sherpa are compared with the measurements. The next-to-leading-order QCD predictions describe the data adequately in shape and normalisation except for regions of phase space such as those with high values of the invariant mass or rapidity separation of the two jets, where the predictions overestimate the data.