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Hydrodynamics simulations are powerful tools for studying fluid behavior under physical forces, enabling extraction of features that reveal key flow characteristics. Traditional post-analysis methods offer high accuracy but incur…

We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…

We have developed a method of solving for multi-species chemical reaction flows in non--equilibrium and self--consistently with the hydrodynamic equations in an expanding FLRW universe. The method is based on a backward differencing scheme…

The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…

The global push to advance Carbon Capture and Sequestration initiatives and green energy solutions, such as geothermal, have thrust new demands upon the current state-of-the-art subsurface fluid simulators. The requirement to be able to…

FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The range of methods include molecular dynamics simulations to sample free…

Multi-fidelity models are of great importance due to their capability of fusing information coming from different numerical simulations, surrogates, and sensors. We focus on the approximation of high-dimensional scalar functions with low…

Central to our understanding of chemical reactivity is the principle of mass conservation, which is fundamental for ensuring physical consistency, balancing equations, and guiding reaction design. However, data-driven computational models…

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning…

Solving chemistry is an integral part of reacting flow simulations, usually dominating the computational cost. Among the different strategies to accelerate the solution of chemistry and to achieve realizable simulations, the use of Dynamic…

This work is concerned with the development of a novel, accurate equation of state for describing partially ionised air plasma in local thermodynamic equilibrium. One key application for this new equation of state is the simulation of…

In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…

Turbulence constitutes an exceptionally complex and irregular flow phenomenon that manifests in liquids, gases, and plasma, making it ubiquitous in both natural processes and engineering applications. Given the relatively modest…

Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such…

The use of machine learning in fluid dynamics is becoming more common to expedite the computation when solving forward and inverse problems of partial differential equations. Yet, a notable challenge with existing convolutional neural…

Fully non-linear equations of motion for dissipative general relativistic multi-fluids can be obtained from an action principle involving the explicit use of lower dimensional matter spaces. More traditional strategies for incorporating…

Numerical simulations of multiphase flows are crucial in numerous engineering applications, but are often limited by the computationally demanding solution of the Navier-Stokes (NS) equations. Here, we present a data-driven workflow where a…

We investigate the behaviour of the lowest nonhydrodynamic modes in a class of holographic models which exhibit an equation of state closely mimicking the one determined from lattice QCD. We calculate the lowest quasinormal mode frequencies…

Considering von Neumann expression for reduced density matrix as thermodynamic entropy of a system strongly coupled to baths, we use nonequilibrium Green's function (NEGF) techniques to derive bath and energy resolved expressions for…

Thermal multi-phase flow simulations are indispensable to understanding the multi-scale and multi-physics phenomena in metal additive manufacturing (AM) processes, yet accurate and robust predictions remain challenging. This book chapter…