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This article introduces a novel numerical approach, based on Finite Volume Techniques, for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and fragmentation components of the collision operator are…
Flow in fractured porous media is of high relevance in a variety of geotechnical applications, given the fact that they ubiquitously occur in nature and that they can have a substantial impact on the hydraulic properties of rock. As a…
The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…
A compact and efficient numerical method is described for studying plane flows of an ideal fluid with a smooth free boundary over a curved and nonuniformly moving bottom. Exact equations of motion in terms of the so-called conformal…
We present a numerical formulation for the solution of non-isothermal, compressible, Navier-Stokes equations with thermal fluctuations to describe mesoscale transport phenomena in multispecies fluid mixtures. The novelty of our numerical…
This work presents a novel numerical investigation of the dynamics of free-boundary flows of viscoelastic liquid membranes. The governing equation describes the balance of linear momentum, in which the stresses include the viscoelastic…
In this study, a numerical model preserving a class of nontrivial steady-state solutions is proposed to predict waves propagation and waves run-up on coastal zones. The numerical model is based on the Saint-Venant system with source terms…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
This paper addresses the floating body problem which consists in studying the interaction of surface water waves with a floating body. We propose a new formulation of the water waves problem that can easily be generalized in order to take…
In the paper we discuss the main features of the software package for numerical simulations of the surface water dynamics. We consider an approximation of the shallow water equations together with the parallel technologies for NVIDIA CUDA…
Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic…
Hydrodynamic simulations have become irreplaceable in modern cosmology for exploring complex systems and making predictions to steer future observations. In Chapter 1, we begin with a philosophical discussion on the role of simulations in…
We formulate hydrodynamic equations and spectrally accurate numerical methods for investigating the role of geometry in flows within two-dimensional fluid interfaces. To achieve numerical approximations having high precision and level of…
In this article, we present a state-of-the-art algorithm for solving the relativistic viscous hydrodynamics equation with the QCD equation of state. The numerical method is based on the second-order Godunov method and has less numerical…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
Hamiltonian splitting methods are an established technique to derive stable and accurate integration schemes in molecular dynamics, in which additional accuracy can be gained using force gradients. For rigid bodies, a tradition exists in…
An effective computer program for three dimensional relativistic hydrodynamical model has been developed. It implements a new approach to the early hot phase of relativistic heavy-ion collisions. The computer program simulates time-space…
We present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid. The main idea is to incorporate Peskin's regularized delta function approach [Acta…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
The anisotropic and heterogeneous $N$-dimensional wave equation, controlled and observed at the boundary, is considered as a port-Hamiltonian system. A recent structure-preserving mixed Galerkin method is applied, leading directly to a…