Related papers: Lagrangian versus Eulerian Methods for Toroidally-…
The Lagrange-Flux schemes are Eulerian finite volume schemes that make use of an approximate Riemann solver in Lagrangian description with particular upwind convective fluxes. They have been recently designed as variant formulations of…
The theory of jet emitting disks (JEDs) provides a mathematical framework for a self-consistent treatment of steady-state accretion and ejection. A large-scale vertical magnetic field threads the accretion disk where magnetic turbulence…
In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube, full-flux-surface, and radially global domains. Two problems are studied: the linear relaxation of zonal flows and…
We analyse the two-dimensional MHD configurations characterising the steady state of the accretion disk on a highly magnetised neutron star. The model we describe has a local character and represents the extension of the crystalline…
In this paper we describe the construction of an efficient probabilistic parameterization that could be used in a coarse-resolution numerical model in which the variation of moisture is not properly resolved. An Eulerian model using a…
Over two hundred protoplanetary disk systems have been resolved by ALMA, and the vast majority suggest the presence of planets. The dust gaps in transition disks are considered evidence of giant planets sculpting gas and dust under…
We introduce a new Lagrangian smooth-particle method to model the growth and drift of pebbles in protoplanetary disks. The Lagrangian nature of the model makes it especially suited to follow characteristics of individual (groups of)…
We begin by placing the Generalized Lagrangian Mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincar\'e (EP) variational framework of fluid dynamics, for an averaged Lagrangian. We then derive a set of approximate…
We apply Gaussian smoothing to obtain mean magnetic field, density, velocity, and magnetic and kinetic energy densities from our numerical model of the interstellar medium, based on three-dimensional magnetohydrodynamic equations in a…
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system…
Hydromagnetic stresses in accretion discs have been the subject of intense theoretical research over the past one and a half decades. Most of the disc simulations have assumed a small initial magnetic field and studied the turbulence that…
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads…
Motivated by challenges in Earth mantle convection, we present a massively parallel implementation of an Eulerian-Lagrangian method for the advection-diffusion equation in the advection-dominated regime. The advection term is treated by a…
A problem of mass flow in the immediate vicinity of a planet embedded in a protoplanetary disk is studied numerically in two dimensions. Large differences in temporal and spatial scales involved suggest that a specialized discretization…
This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal MHD configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that…
In this paper, I mainly prove the following results. For every energy value below the minimum of the first, second and third critical value, each bounded component of the regularized energy hypersurface of the Lagrange problem under some…
Planets are born in protostellar disks, which are now observed with enough resolution to address questions about internal gas flows. Candidates for driving the flows include magnetic forces, but ionization state estimates suggest much of…
We present a divergence-free and $H(div)$-conforming hybridized discontinuous Galerkin (HDG) method and a computationally efficient variant called embedded-HDG (E-HDG) for solving stationary incompressible viso-resistive magnetohydrodynamic…
We develop a computational method based on an Eulerian field called the "reference map", which relates the current location of a material point to its initial. The reference map can be discretized to permit finite-difference simulation of…
We present a high-order accurate reconstructed discontinuous Galerkin (rDG) method in arbitrary Lagrangian-Eulerian (ALE) formulation, for solving two-dimensional compressible flows on moving and deforming domains with unstructured curved…