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We introduce (U)NFV, a modular neural network architecture that generalizes classical finite volume (FV) methods for solving hyperbolic conservation laws. Hyperbolic partial differential equations (PDEs) are challenging to solve,…
We develop a comprehensive Hamiltonian formulation for plasma dynamics that unifies collisionless gyrokinetic and collisional processes. Our framework rigorously describes the evolution of free energy and entropy during the transition from…
Numerical schemes for the solution of the Euler equations have recently been developed, which involve the discretisation of the internal energy equation, with corrective terms to ensure the correct capture of shocks, and, more generally,…
Phase equilibrium calculation, also known as flash calculation, plays significant roles in various aspects of petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development,…
Thermodynamic and flash equilibrium calculations are the cornerstones of simulation process calculations. The iterative approach, a widely used nonlinear problem-solving technique, relies on derivative calculations throughout the procedure…
Smoothed particle hydrodynamics (SPH) has been extensively studied in computer graphics to animate fluids with versatile effects. However, SPH still suffers from two numerical difficulties: the particle deficiency problem, which will…
We present an explicit temporal discretization of particle-in-cell schemes for the Vlasov equation that results in exact energy conservation when combined with an appropriate spatial discretization. The scheme is inspired by a simple,…
We introduce a data-driven diagnostic that combines the singular value decomposition (SVD) with an information-theoretic entropy to quantify the phase-space complexity of perturbed distribution functions in gyrokinetic turbulence. Applying…
We present an efficient strategy for controlling a vast range of non-integrable quantum many body one-dimensional systems that can be merged with state-of-the-art tensor network simulation methods like the density Matrix Renormalization…
Accurately preserving the volume of the dispersed droplets remains a significant challenge in phase-field simulations of droplet-laden turbulence, especially under conditions that feature strong interfacial deformation and breakup. While…
A second-order-accurate finite volume method, hybridized by blending an extended double-flux algorithm and a traditionally conservative scheme, is developed. In this scheme, hybrid convective fluxes as well as hybrid interpolation…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
In this paper, a three-dimensional numerical solver is developed for suspensions of rigid and soft particles and droplets in viscoelastic and elastoviscoplastic (EVP) fluids. The presented algorithm is designed to allow for the first time…
We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…
In this work, Entropy-Stable (ES) schemes are formulated for the multicomponent compressible Euler equations. Entropy-conservative (EC) and ES fluxes are derived. Particular attention is paid to the limit case of zero partial densities…
We present the Photon-Plasma code, a modern high order charge conserving particle-in-cell code for simulating relativistic plasmas. The code is using a high order implicit field solver and a novel high order charge conserving interpolation…
The accurate prediction of occurrence and strength of kinetic instabilities in plasmas remains a significant challenge in nuclear fusion research. To accurately capture the plasmas dynamics one is required to solve the Vlasov equation for…
Melting and solidification processes are often affected by natural convection of the liquid, posing a multi-physics problem involving fluid flow, convective and diffusive heat transfer, and phase-change reactions. Enthalpy methods formulate…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
It is known that Flux Corrected Transport algorithms can produce entropy-violating solutions of hyperbolic conservation laws. Our purpose is to design flux correction with maximal antidiffusive fluxes to obtain entropy solutions of scalar…