2,989 research outputs found
A Two-moment Radiation Hydrodynamics Module in Athena Using a Time-explicit Godunov Method
We describe a module for the Athena code that solves the gray equations of
radiation hydrodynamics (RHD), based on the first two moments of the radiative
transfer equation. We use a combination of explicit Godunov methods to advance
the gas and radiation variables including the non-stiff source terms, and a
local implicit method to integrate the stiff source terms. We adopt the M1
closure relation and include all leading source terms. We employ the reduced
speed of light approximation (RSLA) with subcycling of the radiation variables
in order to reduce computational costs. Our code is dimensionally unsplit in
one, two, and three space dimensions and is parallelized using MPI. The
streaming and diffusion limits are well-described by the M1 closure model, and
our implementation shows excellent behavior for a problem with a concentrated
radiation source containing both regimes simultaneously. Our operator-split
method is ideally suited for problems with a slowly varying radiation field and
dynamical gas flows, in which the effect of the RSLA is minimal. We present an
analysis of the dispersion relation of RHD linear waves highlighting the
conditions of applicability for the RSLA. To demonstrate the accuracy of our
method, we utilize a suite of radiation and RHD tests covering a broad range of
regimes, including RHD waves, shocks, and equilibria, which show second-order
convergence in most cases. As an application, we investigate radiation-driven
ejection of a dusty, optically thick shell in the interstellar medium (ISM).
Finally, we compare the timing of our method with other well-known iterative
schemes for the RHD equations. Our code implementation, Hyperion, is suitable
for a wide variety of astrophysical applications and will be made freely
available on the Web.Comment: 30 pages, 29 figures, accepted for publication in ApJ
Institute for Computational Mechanics in Propulsion (ICOMP)
The Institute for Computational Mechanics in Propulsion (ICOMP) is a combined activity of Case Western Reserve University, Ohio Aerospace Institute (OAI) and NASA Lewis. The purpose of ICOMP is to develop techniques to improve problem solving capabilities in all aspects of computational mechanics related to propulsion. The activities at ICOMP during 1991 are described
An acoustic-transport splitting method for the barotropic Baer-Nunziato two-phase flow model*
This work focuses on the numerical approximation of the barotropic Baer-Nunziato two-phase flow model. We propose a numerical scheme that relies on an operator splitting method corresponding to a separate treatment of the acoustic and the material transport phenomena. In the subsonic case, this also corresponds to a separate treatment of the fast and the slow propagation phenomena. This approach follows the lines of the implicit-explicit schemes developed in [8]. The operator splitting enable the use of time steps that are no longer constrained by the sound velocity thanks to an implicit treatment of the acoustic waves, while maintaining accuracy in the subsonic regime thanks to an explicit treatment of the material waves. In the present setting, a particular attention will be also given to the discretization of the non-conservative terms that figure in the two-phase model. We prove that the proposed numerical strategy is positivity preserving for the volume fractions and the partial masses. The scheme is tested against several one-dimensional test cases including flows featuring vanishing phases
A robust high-order Lagrange-projection like scheme with large time steps for the isentropic Euler equations
International audienceWe present an extension to high-order of a first-order Lagrange-projection like method for the approximation of the Euler equations introduced in Coquel et al. (Math. Comput., 79 (2010), pp. 1493–1533). The method is based on a decomposition between acoustic and transport operators associated to an implicit-explicit time integration, thus relaxing the constraint of acoustic waves on the time step. We propose here to use a discontinuous Galerkin method for the space approximation. Considering the isentropic Euler equations, we derive conditions to keep positivity of the mean value of density and to satisfy a discrete entropy inequality in each element of the mesh at any approximation order in space. These results allow to design limiting procedures to restore these properties at nodal values within elements. Numerical experiments support the conclusions of the analysis and highlight stability and robustness of the present method, while it allows the use of large time steps
Applications of Various Methods of Analysis to Combustion Instabilities in Solid Propellant Rockets
Instabilities of motions in a combustion chamber are consequences of the coupled dynamics of
combustion processes and of the flow in the chamber. The extreme complexities of the problem
always require approximations of various sorts to make progress in understanding the
mechanisms and behavior of combustion instabilities. This paper covers recent progress in the
subject, mainly summarizing efforts in two areas: approximate analysis based on a form of
Galerkin's method, particularly useful for understanding the global linear and nonlinear
dynamics of combustion instabilities and numerical simulations intended to accommodate as
fully as possible fundamental chemical processes in both the condensed and gaseous phases.
One purpose of current work is to bring closer together these approaches to produce more
comprehensive and detailed realistic results applicable to the interpretation of observations
and for design of new rockets for both space and military applications. Particularly important
are the goals of determining the connections between chemical composition and instabilities;
and the influences of geometry on nonlinear behavior
Finite Element Flux-Corrected Transport (FEM-FCT) for the Euler and Navier-Stokes equations
A high resolution finite element method for the solution of problems involving high speed compressible flows is presented. The method uses the concepts of flux-corrected transport and is presented in a form which is suitable for implementation on completely unstructured triangular or tetrahedral meshes. Transient and steady state examples are solved to illustrate the performance of the algorithm
A time splitting projection scheme for compressible two-phase flows. Application to the interaction of bubbles with ultrasound waves
This paper is focused on the numerical simulation of the interaction of an ultrasound wave with a bubble. Our interest is to develop a fully compressible solver in the two phases and to account for surface tension effects.
As the volume oscillation of the bubble occurs in a low Mach number regime, a specific care must be paid to the effectiveness of the numerical method which is chosen to solve the compressible Euler equations. Three different numerical solvers, an explicit HLLC (Harten–Lax–van Leer-Contact) solver [48], a preconditioning explicit HLLC solver [14] and the compressible projection method , and , are described and assessed with a one dimensional spherical benchmark. From this preliminary test, we can conclude that the compressible projection method outclasses the other two, whether the spatial accuracy or the time step stability are considered.
Multidimensional numerical simulations are next performed. As a basic implementation of the surface tension leads to strong spurious currents and numerical instabilities, a specific velocity/pressure time splitting is proposed to overcome this issue. Numerical evidences of the efficiency of this new numerical scheme are provided, since both the accuracy and the stability of the overall algorithm are enhanced if this new time splitting is used. Finally, the numerical simulation of the interaction of a moving and deformable bubble with a plane wave is presented in order to bring out the ability of the new method in a more complex situation
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