Related papers: Hyperbolic Self-Gravity Solver for Large Scale Hyd…
We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's…
This is a short review of a series of papers which, in collaboration with Yue Ma, establish several novel existence results for systems of coupled wave-Klein-Gordon equation. Our method, the Hyperbolic Hyperboloidal Method, has allowed us…
The solution of the Poisson equation is a ubiquitous problem in computational astrophysics. Most notably, the treatment of self-gravitating flows involves the Poisson equation for the gravitational field. In hydrodynamics codes using…
Accurate simulations of flows in stellar interiors are crucial to improving our understanding of stellar structure and evolution. Because the typically slow flows are merely tiny perturbations on top of a close balance between gravity and…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
At the heart of any method for computational fluid dynamics lies the question of how the simulated fluid should be discretized. Traditionally, a fixed Eulerian mesh is often employed for this purpose, which in modern schemes may also be…
Methods to solve the relativistic hydrodynamic equations are a key computational kernel in a large number of astrophysics simulations and are crucial to understanding the electromagnetic signals that originate from the merger of…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
Versions of parameterized pseudo-Newtonian gravity theories specially designed for cosmology have been introduced in recent cosmology literature. The modifications demand a zero-pressure fluid in the context of versions of modified…
We present a new implementation of the SFUMATO code, called SFUMATO#, for solving self-gravitational radiation hydrodynamics problems using adaptive mesh refinement (AMR) with the CUDA/HIP programming frameworks. The code incorporates a…
We utilise a form for the Hubble parameter to generate a number of solutions to the Einstein field equations with variable cosmological constant and variable gravitational constant in the presence of a bulk viscous fluid. The Hubble law…
We consider the fully-coupled McKean-Vlasov equation with multi-time-scale potentials, and all the coefficients depend on the distributions of both the slow component and the fast motion. By studying the smoothness of the solution of the…
Self-gravity plays an important role in the evolution of rotationally supported systems such as protoplanetary disks, accretion disks around black holes, or galactic disks, as it can both feed turbulence or lead to gravitational…
In this paper, a new efficient and generalized consistency correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking…
A homogenization approach is proposed for the treatment of porous wall boundary conditions in the computation of compressible viscous flows. Like any other homogenization approach, it eliminates the need for pore-resolved fluid meshes and…
The geodesy of irregularly shaped small bodies presents fundamental challenges for gravitational field modeling, particularly as deep space exploration missions increasingly target asteroids and comets. Traditional approaches suffer from…
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the…
Variable density incompressible flows are governed by parabolic equations. The artificial compressibility method makes these equations hyperbolic-type, which means that they can be solved using techniques developed for compressible flows,…
In this paper the quantum hydrodynamic approach for the KGE owning a perturbative self-interaction term is developed. The generalized model to non-Euclidean space-time allows to determine the quantum energy impulse tensor density of mesons…