1,057 research outputs found
MAESTRO: An Adaptive Low Mach Number Hydrodynamics Algorithm for Stellar Flows
Many astrophysical phenomena are highly subsonic, requiring specialized
numerical methods suitable for long-time integration. In a series of earlier
papers we described the development of MAESTRO, a low Mach number stellar
hydrodynamics code that can be used to simulate long-time, low-speed flows that
would be prohibitively expensive to model using traditional compressible codes.
MAESTRO is based on an equation set derived using low Mach number asymptotics;
this equation set does not explicitly track acoustic waves and thus allows a
significant increase in the time step. MAESTRO is suitable for two- and
three-dimensional local atmospheric flows as well as three-dimensional
full-star flows. Here, we continue the development of MAESTRO by incorporating
adaptive mesh refinement (AMR). The primary difference between MAESTRO and
other structured grid AMR approaches for incompressible and low Mach number
flows is the presence of the time-dependent base state, whose evolution is
coupled to the evolution of the full solution. We also describe how to
incorporate the expansion of the base state for full-star flows, which involves
a novel mapping technique between the one-dimensional base state and the
Cartesian grid, as well as a number of overall improvements to the algorithm.
We examine the efficiency and accuracy of our adaptive code, and demonstrate
that it is suitable for further study of our initial scientific application,
the convective phase of Type Ia supernovae.Comment: Accepted to Astrophysical Journal Suppliment (http://iop.org). 56
pages, 15 figures
Hybrid finite difference/finite element immersed boundary method
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian
description of the structural deformations, stresses, and forces along with an Eulerian description of the
momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary
methods described immersed elastic structures using systems of flexible fibers, and even now, most
immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This
work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian
variables that facilitates independent spatial discretizations for the structure and background grid. This
approach employs a finite element discretization of the structure while retaining a finite difference scheme
for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively
contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases
in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors
that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes.
The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse
structural meshes with the immersed boundary method. This work also contrasts two different weak forms
of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations
facilitated by our coupling approach
A new numerical strategy with space-time adaptivity and error control for multi-scale streamer discharge simulations
This paper presents a new resolution strategy for multi-scale streamer
discharge simulations based on a second order time adaptive integration and
space adaptive multiresolution. A classical fluid model is used to describe
plasma discharges, considering drift-diffusion equations and the computation of
electric field. The proposed numerical method provides a time-space accuracy
control of the solution, and thus, an effective accurate resolution independent
of the fastest physical time scale. An important improvement of the
computational efficiency is achieved whenever the required time steps go beyond
standard stability constraints associated with mesh size or source time scales
for the resolution of the drift-diffusion equations, whereas the stability
constraint related to the dielectric relaxation time scale is respected but
with a second order precision. Numerical illustrations show that the strategy
can be efficiently applied to simulate the propagation of highly nonlinear
ionizing waves as streamer discharges, as well as highly multi-scale nanosecond
repetitively pulsed discharges, describing consistently a broad spectrum of
space and time scales as well as different physical scenarios for consecutive
discharge/post-discharge phases, out of reach of standard non-adaptive methods.Comment: Support of Ecole Centrale Paris is gratefully acknowledged for
several month stay of Z. Bonaventura at Laboratory EM2C as visiting
Professor. Authors express special thanks to Christian Tenaud (LIMSI-CNRS)
for providing the basis of the multiresolution kernel of MR CHORUS, code
developed for compressible Navier-Stokes equations (D\'eclaration d'Invention
DI 03760-01). Accepted for publication; Journal of Computational Physics
(2011) 1-2
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