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The migration of growing protoplanets depends on the thermodynamics of the ambient disc. Standard modelling, using locally isothermal discs, indicate in the low planet mass regime an inward (type-I) migration. Taking into account…
In this paper we briefly discuss the ways in which angular momentum transport is included in simulations of non-self-gravitating accretion disks, concentrating on disks in close binaries. Numerical approaches fall in two basic categories;…
We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a…
In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any…
We revisit our original papers on the burst mode of accretion by incorporating a detailed energy balance equation into a thin-disk model for the formation and evolution of circumstellar disks around low-mass protostars.Our model includes…
We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…
(abridged) Context: The vertical shear instability (VSI) is a promising mechanism to generate turbulence and transport angular momentum in protoplanetary discs. While most recent work has focused on adding more complex physics, the…
The long-term evolution of a circumstellar disk starting from its formation and ending in the T Tauri phase was simulated numerically with the purpose of studying the evolution of dust in the disk with distinct values of viscous…
Models of the formation, evolution and photoevaporation of circumstellar disks are an essential ingredient in many theories of the formation of planetary systems. The ratio of disk mass over stellar mass in the circumstellar phase of a disk…
This work presents algorithms for the efficient implementation of discontinuous Galerkin methods with explicit time stepping for acoustic wave propagation on unstructured meshes of quadrilaterals or hexahedra. A crucial step towards…
In this paper, we extend our previous analysis (Lodato & Rice 2004) of the transport properties induced by gravitational instabilities in cooling, gaseous accretion discs to the case where the disc mass is comparable to the central object.…
Numerical experiments are the primary method of studying the evolution of circumbinary disks due to the strong nonlinearities involved. Many circumbinary simulations also require the use of numerical mass sinks: source terms which prevent…
We present the latest development of the disk gravitational instability and fragmentation model, originally introduced by us to explain episodic accretion bursts in the early stages of star formation. Using our numerical hydrodynamics model…
The Reynolds-averaged Navier-Stokes (RANS) equations provide a computationally efficient method for solving fluid flow problems in engineering applications. However, the use of closure models to represent turbulence effects can reduce their…
We propose a sensor-restrained model for the shear viscosity term within the localized artificial diffusivity (LAD) scheme to stabilize compressible large-eddy simulations with low-pressure-core vortical structures. LAD methods are used in…
The rapid depletion of dust particles in protoplanetary disks limits the time available for planetesimal formation, as solids are typically accreted onto the central star before dust particles can undergo substantial growth. Dust traps…
We present a meshless numerical method for simulating the dynamics of axisymmetric vesicles in a viscous medium. Key innovations include: (1) adaptive reparameterization based on local length scales, reducing the number of required…
We develop an analytical model for the accretion and gravitational drag on a point mass that moves hypersonically in the midplane of a gaseous disk with a Gaussian vertical density stratification. Such a model is of interest for studying…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
A novel inline data compression method is presented for single-precision vectors in three dimensions. The primary application of the method is for accelerating computational physics calculations where the throughput is bound by memory…