Joshua McConnell | Searcharxiv

arXiv2026

Analysis, thermodynamics, and a numerical solver for a pressure-temperature equilibrium closure of the four-equation model

We analyze an often used closure model for multi-material hydrodynamics where pressure-temperature equilibrium (PTE) is assumed for every state; emphasis is placed on tabular equations of state. This multi-material model is often referred to as the four-equation model. The identification of the admissible set is presented and is proven to be convex, setting the foundation for development of invariant-domain preserving methods for this model. A novel numerical method is presented for solving the highly nonlinear system for the equilibrated pressure and temperature with an arbitrary number of materials. This new method is compared with some traditional iterative solvers through a collection of different tests. Additionally, we provide a detailed analysis of the thermodynamics of the mixture model for general equations of state and prove existence and uniqueness of the pressure-temperature equilibrium solution under some thermodynamic assumptions.

math.NA↗

arXiv2020

Mesoscopic modeling of heptane: A surface tension calculation

Accurate and efficient flow models for hydrocarbons are important in the development of enhanced geotechnical engineering for energy source recovery and carbon capture & storage in low-porosity, low-permeability rock formations. This work reports an atomistically-validated, mesoscopic model for heptane based on a many-body dissipative particle dynamics (mDPD) method. In this model, each heptane molecule is coarse-grained in one mDPD bead and the mDPD model parameters are calibrated with a rigorous approach using reference data, including experimental measurements and/or molecular dynamics (MD) simulations. Results show that this mDPD model accurately predicts the bulk pressure-density relation of heptane and surface tension. Notice that our approach can be used to calibrate the mDPD model for other hydrocarbons as well, though heptane is chosen as a representative source fluid for its abundance in source rocks. Further, our timing test indicates that the mDPD model is three orders of magnitude faster than its MD counterpart for simulations of bulk heptane in equivalent volumes. Overall, this work serves as a key prerequisite for the development of accurate and efficient mesoscale models for the flow of hydrocarbons confined in mesoporous rock formations.

physics.comp-ph↗