相关论文: A Fully Explicit Integrator for Modeling Astrophys…
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characterized by a small parameter $\varepsilon$. In this work, we…
Atmospheric escape is crucial to understand the evolution of planets in and out of the Solar system and to interpret atmospheric observations. While hydrodynamic escape simulations have been actively developed incorporating detailed…
For astrophysical reacting flows, operator splitting is commonly used to couple hydrodynamics and reactions. Each process operates independent of one another, but by staggering the updates in a symmetric fashion (via Strang splitting)…
Compact Runge-Kutta (cRK) Discontinuous Galerkin (DG) methods, recently introduced in [Q. Chen, Z. Sun, and Y. Xing, SIAM J. Sci. Comput. SIAM J. Sci. Comput., 46: A1327-A1351, 2024], are a variant of RKDG methods for solving hyperbolic…
A mixed accuracy framework for Runge--Kutta methods presented in [Grant, JSC 2022] has been shown to speed up the computation in diagonally implicit Runge--Kutta (DIRK) methods by using less expensive low accuracy approaches for the…
Solving the Bhatnagar-Gross-Krook (BGK) equation with a stochastic particle approach enables efficient and flexible simulations of flows in the transition regime, between continuum and free molecular flow. However, the usual first-order…
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…
In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We…
Global spectral analysis (GSA) is used as a tool to test the accuracy of numerical methods with the help of canonical problems of convection and convection-diffusion equation which admit exact solutions. Similarly, events in turbulent flows…
We describe a new computational method for the numerically stable particle-based simulation of open-boundary flows, including volume conserving chemical reactions. The novel method is validated for the case of heterogeneous catalysis…
This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and component-partitioned…
The Landau-Lifshitz equation provides an efficient way to account for the effects of radiation reaction without acquiring the non-physical solutions typical for the Lorentz-Abraham-Dirac equation. We solve the Landau-Lifshitz equation in…
Reservoir computing (RC) is a state-of-the-art machine learning method that makes use of the power of dynamical systems (the reservoir) for real-time inference. When using biological complex systems as reservoir substrates, it serves as a…
Reacting astrophysical flows can be challenging to model because of the difficulty in accurately coupling hydrodynamics and reactions. This can be particularly acute during explosive burning or at high temperatures where nuclear statistical…
The simulation of chemical kinetics involving multiple scales constitutes a modeling challenge (from ordinary differential equations to Markov chain) and a computational challenge (multiple scales, large dynamical systems, time step…
The second-order extended stability Factorized Runge-Kutta-Chebyshev (FRKC2) class of explicit schemes for the integration of large systems of PDEs with diffusive terms is presented. FRKC2 schemes are straightforward to implement through…
We propose a new method to solve the relativistic hydrodynamic equations based on implicit Runge-Kutta methods with a locally optimized fixed-point iterative solver. For numerical demonstration, we implement our idea for ideal hydrodynamics…
A numerical method for integrating the equations describing a dynamically coupled system made of a fluid and cosmic-rays is developed. In smooth flows the effect of CR pressure is accounted for by modification of the characteristic…
We demonstrate the first implementation of recently-developed fast explicit kinetic integration algorithms on modern graphics processing unit (GPU) accelerators. Taking as a generic test case a Type Ia supernova explosion with an extremely…
Directed flow in ultrarelativistic nucleus-nucleus collisions is analyzed using the reaction plane from elliptic flow, which reduces the bias from nonflow effects. We combine this method with the determination of elliptic flow from Lee-Yang…