Related papers: The Pencil Code, a modular MPI code for partial di…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
This paper focuses on multirate time-domain simulations of power system models. It proposes a matrix pencil-based approach to evaluate the spurious numerical deformation introduced into power system dynamics by a given multirate integration…
We report on the development of a test-particle based kinetic Monte Carlo code for large systems and its application to simulate matter in the continuum regime. Our code combines advantages of the Direct Simulation Monte Carlo and the…
In many plasmas, in particular in space science, protons govern much of the essential physics. Minority ions, suprathermal tails, and electrons at times account for additional details. However, electron effects usually appear on much…
Particle-in-Cell (PIC) simulation codes have wide applicability to first-principles modeling of multidimensional nonlinear plasma phenomena, including wake-field accelerators. This review addresses both finite difference and pseudo-spectral…
Wet particle separation is widely used in mineral processing and plastic recycling to separate mixtures of particulate materials into further usable fractions due to density differences. This work presents efforts aiming to numerically…
We represent an algorithm reducing a big class of systems of ($M+1$)-dimensional nonlinear partial differential equations (PDEs) to the systems of $M$-dimensional first order PDEs. Thus, we integrate the original system with respect to only…
A high-order scheme for direct numerical simulations of turbulent combustion is discussed. Its implementation in the massively parallel and publicly available Pencil Code is validated with the focus on hydrogen combustion. Ignition delay…
Recent releases of open-source research codes and solvers for numerically solving partial differential equations in Python present a great opportunity for educators to integrate these codes into the classroom in a variety of ways. The ease…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…
We describe a new electrostatic Particle-In-Cell (PIC) code in curvilinear geometry called Curvilinear PIC (CPIC). The code models the microscopic (kinetic) evolution of a plasma with the PIC method, coupled with an adaptive computational…
Elliptic partial differential equations (PDEs) frequently arise in continuum descriptions of physical processes relevant to science and engineering. Multilevel preconditioners represent a family of scalable techniques for solving discrete…
We describe the Stagger Code for simulations of magneto-hydrodynamic (MHD) systems. This is a modular code with a variety of physics modules that will let the user run simulations of deep stellar atmospheres, sunspot formation, stellar…
For the self-consistent description of various plasma sources operated in the low-pressure (nonlocal, kinetic) regime, the Particle-In-Cell simulation approach, combined with the Monte Carlo treatment of collision processes (PIC/MCC), has…
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…
The Mancha3D code is a versatile tool for numerical simulations of magnetohydrodynamic processes in solar/stellar atmospheres. The code includes non-ideal physics derived from plasma partial ionization, a realistic equation of state and…
Multidimensional hydrodynamical simulations have transformed the study of stellar interiors over the past few decades. Most codes developed during that time use the anelastic approximation, which fixes the thermal structure of simulations…
We present a Fortran 95 code for simulating the evolution of astrophysical systems using particles to represent the underlying fluid flow. The code is designed to be versatile, flexible and extensible, with modular options that can be…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…