Related papers: Hyperbolic Self-Gravity Solver for Large Scale Hyd…
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…
We implement general relativistic hydrodynamics in the moving-mesh code AREPO. We also couple a solver for the Einstein field equations employing the conformal flatness approximation. The implementation is validated by evolving isolated…
The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving…
In order to determine the steady-state subcritical gravity-capillary waves that are produced by potential flow past a wave-making body, it is typically necessary to impose a radiation condition that allows for capillary waves upstream, but…
In recent time, by working in a plane with the metric associated with wave equation (the Special Relativity non-definite quadratic form), a complete formalization of space-time trigonometry and a Cauchy-like integral formula have been…
We present a numerical method to solve the equations of general relativistic hydrodynamics in a given external gravitational field. The method is based on a generalization of Roe's approximate Riemann solver for the non relativistic Euler…
Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…
We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two…
A new method that solves concurrently the multi-fluid and Maxwell's equations has been developed for plasma simulations. By calculating the stress tensor in the multi-fluid momentum equation by means of computational particles moving in a…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
We consider the thin-film equation with linear mobility and a stabilizing second-order porous-medium type term modeling gravity. The model admits self-similar solutions, and our goal is to analyze their stability. We reformulate the problem…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
Hyperbolic spaces have increasingly been recognized for their outstanding performance in handling data with inherent hierarchical structures compared to their Euclidean counterparts. However, learning in hyperbolic spaces poses significant…
We present the design of a multiscale parareal method for kinetic equations in the fluid dynamic regime. The goal is to reduce the cost of a fully kinetic simulation using a parallel in time procedure. Using the multiscale property of…
We present a new code, CASTRO, that solves the multicomponent compressible hydrodynamic equations for astrophysical flows including self-gravity, nuclear reactions and radiation. CASTRO uses an Eulerian grid and incorporates adaptive mesh…
The constraints of the superfield method in two-dimensional supergravity are adapted to allow for nonvanishing bosonic torsion. As the analysis of the Bianchi identities reveals, a new vector superfield is encountered besides the well-known…
We investigate the possibility to approximate relativistic effects in hydrodynamical simulations of stellar core collapse and post-bounce evolution by using a modified gravitational potential in an otherwise standard Newtonian hydrodynamic…
A major limitation of the weakly compressible approaches to simulate incompressible flows is the appearance of artificial acoustic waves that introduce a large mass conservation error and lead to spurious oscillations in the force…