Related papers: The Pencil Code, a modular MPI code for partial di…
We present a new magnetohydrodynamic (MHD) simulation code with the aim of providing accurate numerical solutions to astrophysical phenomena where discontinuities, shock waves, and turbulence are inherently important. The code implements…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Stable, accurate, divergence-free simulation of magnetized supersonic turbulence is a severe test of numerical MHD schemes and has been surprisingly difficult to achieve due to the range of flow conditions present. Here we present a new,…
Multi-particle collision dynamics (MPCD) is a mesoscopic simulation method to simulate fluid particle-like flows. MPCD has been widely used to simulate various problems in condensed matter. In this study, hydrostatic behavior of gas in the…
Numerical approximations of partial differential equations (PDEs) are routinely employed to formulate the solution of physics, engineering, and mathematical problems involving functions of several variables, such as the propagation of heat…
Patchy particles is the name given to a large class of systems of mesoscopic particles characterized by a repulsive core and a discrete number of short-range and highly directional interaction sites. Numerical simulations have contributed…
Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…
Abstract differential-algebraic equations (ADAEs) of a semilinear type are studied. Theorems on the existence and uniqueness of solutions and the maximal interval of existence, on the global solvability of the ADAEs, the boundedness of…
Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…
Parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) have a wide range of applications. In particular, high-dimensional PDEs with gradient-dependent nonlinearities appear often in the…
Complex plasmas are low-temperature plasmas that contain micrometer-size particles in addition to the neutral gas particles and the ions and electrons that make up the plasma. The microparticles interact strongly and display a wealth of…
Particle-in-cell merging algorithms aim to resample dynamically the six-dimensional phase space occupied by particles without distorting substantially the physical description of the system. Whereas various approaches have been proposed in…
The exponential growth of the power of modern digital computers is based upon the miniaturisation of vast nanoscale arrays of electronic switches, but this will be eventually constrained by fabrication limits and power dissipation. Chemical…
Fractional and tempered fractional partial differential equations (PDEs) are effective models of long-range interactions, anomalous diffusion, and non-local effects. Traditional numerical methods for these problems are mesh-based, thus…
A simulation package employing a Particle in Cell (PIC) method is developed to study the high current beam transport and the dynamics of plasmas. This package includes subroutines those are suited for various planned projects at University…
The main objective of this talk is to develop a matrix pencil approach for the study of an initial value problem of a class of singular linear matrix differential equations whose coefficients are constant matrices. By using matrix pencil…
In this contribution we discuss about numerical modeling of nebulae. In particular we emphasize on the dynamical evolution of an HII region and the chemical structure of a Photodissociation region. We do this using the Smoothed Particles…
Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be…
Particle methods are less computationally efficient than grid based numerical solution of the Navier Stokes equation. However, they have important advantages including rigorous mass conservation, momentum conservation and isotropy. In…
Over the past decades, multiple gyrokinetic codes have shown to be able to simulate turbulence and associated transport in the core of Tokamak devices. However, their application to the edge and scrape-off layer (SOL) region presents…