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We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the…
Large regions of giant planets are thought to possess unstable thermal gradients stabilised by gradients in heavy-element composition. The fluid can then develop semi-convection, a double-diffusive instability driven by the unequal…
A volumetric lattice Boltzmann (LB) method is developed for the particle-resolved direct numerical simulation of thermal particulate flows with conjugate heat transfer. This method is devised as a single-domain approach by applying the…
A three-dimensional model of polydisperse reactive sedimentation is developed by means of a multilayer shallow water approach. The model consists of a variety of solid particles of different sizes and densities, and substrates diluted in…
We propose a multiscale computational method for thin-layer flows of complex fluids, termed the synchronized molecular dynamics (SMD) method, which directly couples local molecular dynamics (MD) simulations with a macroscopic lubrication…
We propose the -- to the best of our knowledge -- first fully functional implementation of the ``Separation by a Convex Body'' (SCB) approach first outlined in Grzybowski et al. [1] for classification, separating two data sets using an…
We address in this paper a model for the simulation of turbulent deflagrations in industrial applications. The flow is governed by the Euler equations for a variable composition mixture and the combustion modelling is based on a…
The Serre-Green-Naghdi (SGN) equations provide a valuable framework for modelling fully nonlinear and weakly dispersive shallow-water flows. However, their elliptic formulation can considerably increase the computational cost compared to…
The results of Direct Numerical Simulations of the oscillatory flow over a cohesionless bed of spherical particles, mimicking sediment grains, are described. The flow around the sediment particles is explicitly computed by using the…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
Fluid thermodynamics underpins atmospheric dynamics, climate science, industrial applications, and energy systems. However, direct numerical simulations (DNS) of such systems can be computationally prohibitive. To address this, we present a…
The energy balance of a partially molten rocky planet can be expressed as a non-linear diffusion equation using mixing length theory to quantify heat transport by both convection and mixing of the melt and solid phases. In this formulation…
Biomolecular condensates play essential roles in cellular processes, and recent efforts have focused on understanding their assembly and rational design principles. In this study, we have employed an explicit-solvent minimal statistical…
An abstract framework is developed that enables the analysis of algebraically stabilized discretizations in a unified way. This framework is applied to a discretization of this kind for convection-diffusion-reaction equations. The…
We prove existence, uniqueness, and regularity for a reaction-diffusion system of coupled bulk-surface equations on a moving domain modelling receptor-ligand dynamics in cells. The nonlinear coupling between the three unknowns is through…
In robot swarms operating under highly restrictive sensing and communication constraints, individuals may need to use direct physical proximity to facilitate information exchange. However, in certain task-related scenarios, this requirement…
Mixture fraction-based models are widely employed for predicting turbulent non-premixed combustion processes due to their cost-effectiveness and well-established subfilter closure. In these models, the transport of reactive scalars in…
In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in…