Related papers: A Fully Explicit Integrator for Modeling Astrophys…

Use of explicit methods for simulating electrical circuits, especially for power electronics applications, is described. Application of the forward Euler method to a half-wave rectifier is discussed, and the limitations of a fixed-step…

In this paper, we propose a class of high-order and energy-stable implicit-explicit relaxation Runge-Kutta (IMEX RRK) schemes for solving the phase-field gradient flow models. By incorporating the scalar auxiliary variable (SAV) method, the…

We present the Minimally-Implicit Runge-Kutta (MIRK) methods for the numerical evolution of the resistive relativistic magnetohydrodynamic (RRMHD) equations, following the approach proposed by Komissarov (2007) of an augmented system of…

In this paper we describe a numerical algorithm for integrating the multicomponent, reacting, compressible Navier-Stokes equations, targeted for direct numerical simulation of combustion phenomena. The algorithm addresses two shortcomings…

Exascale computing enables high-fidelity simulations of chemically reactive flows in practical geometries and conditions, and paves the way for valuable insights that can optimize combustion processes, ultimately reducing emissions and…

Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…

Numerical radiation-hydrodynamics (RHD) for non-relativistic flows is a challenging problem because it encompasses processes acting over a very broad range of timescales, and where the relative importance of these processes often varies by…

Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…

We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…

We present an effective system for simulating dust continuum observations by radiative transfer simulations. By using workflow management system RENKEI-WFT, we utilized distributed computing resources and automated a sequence of…

Implicit Runge--Kutta (IRK) methods are highly effective for solving stiff ordinary differential equations (ODEs) but can be computationally expensive for large-scale problems due to the need of solving coupled algebraic equations at each…

Runge-Kutta methods have an irreplaceable position among numerical methods designed to solve ordinary differential equations. Especially, implicit ones are suitable for approximating solutions of stiff initial value problems. We propose a…

In this work, we introduce DeepFlame, an open-source C++ platform with the capabilities of utilising machine learning algorithms and pre-trained models to solve for reactive flows. We combine the individual strengths of the computational…

We present a new family of relativistic lattice kinetic schemes for the efficient simulation of relativistic flows in both strongly-interacting (fluid) and weakly-interacting (rarefied gas) regimes. The method can also deal with both…

The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…

Applied to the master equation, the usual numerical integration methods, such as Runge-Kutta, become inefficient when the rates associated with various transitions differ by several orders of magnitude. We introduce an integration scheme…

We consider the solution of large stiff systems of ordinary differential equations with explicit exponential Runge--Kutta integrators. These problems arise from semi-discretized semi-linear parabolic partial differential equations on…

We propose a numerical methodology for the numerical simulation of distinct, interacting physical processes described by a combination of compressible, inert and reactive forms of the Euler equations, multiphase equations and elastoplastic…

We extend ring-polymer molecular dynamics (RPMD) to allow for the direct simulation of general, electronically non-adiabatic chemical processes. The kinetically constrained (KC) RPMD method uses the imaginary-time path-integral…

We study the coupling of hydrodynamics and reactions in simulations of the double detonation model for Type Ia supernovae. When assessing the convergence of simulations, the focus is usually on spatial resolution; however, the method of…