547 research outputs found
First-Order System Least Squares and the Energetic Variational Approach for Two-Phase Flow
This paper develops a first-order system least-squares (FOSLS) formulation
for equations of two-phase flow. The main goal is to show that this
discretization, along with numerical techniques such as nested iteration,
algebraic multigrid, and adaptive local refinement, can be used to solve these
types of complex fluid flow problems. In addition, from an energetic
variational approach, it can be shown that an important quantity to preserve in
a given simulation is the energy law. We discuss the energy law and inherent
structure for two-phase flow using the Allen-Cahn interface model and indicate
how it is related to other complex fluid models, such as magnetohydrodynamics.
Finally, we show that, using the FOSLS framework, one can still satisfy the
appropriate energy law globally while using well-known numerical techniques.Comment: 22 pages, 8 figures submitted to Journal of Computational Physic
An Implicit Scheme for Ohmic Dissipation with Adaptive Mesh Refinement
An implicit method for the ohmic dissipation is proposed. The proposed method
is based on the Crank-Nicolson method and exhibits second-order accuracy in
time and space. The proposed method has been implemented in the SFUMATO
adaptive mesh refinement (AMR) code. The multigrid method on the grids of the
AMR hierarchy converges the solution. The convergence is fast but depends on
the time step, resolution, and resistivity. Test problems demonstrated that
decent solutions are obtained even at the interface between fine and coarse
grids. Moreover, the solution obtained by the proposed method shows good
agreement with that obtained by the explicit method, which required many time
steps. The present method reduces the number of time steps, and hence the
computational costs, as compared with the explicit method.Comment: Accepted for publication in PASJ. 8 pages, 11 figure
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
We present the first high order one-step ADER-WENO finite volume scheme with
Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial
accuracy is obtained through a WENO reconstruction, while a high order one-step
time discretization is achieved using a local space-time discontinuous Galerkin
predictor method. Due to the one-step nature of the underlying scheme, the
resulting algorithm is particularly well suited for an AMR strategy on
space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR
property has been implemented 'cell-by-cell', with a standard tree-type
algorithm, while the scheme has been parallelized via the Message Passing
Interface (MPI) paradigm. The new scheme has been tested over a wide range of
examples for nonlinear systems of hyperbolic conservation laws, including the
classical Euler equations of compressible gas dynamics and the equations of
magnetohydrodynamics (MHD). High order in space and time have been confirmed
via a numerical convergence study and a detailed analysis of the computational
speed-up with respect to highly refined uniform meshes is also presented. We
also show test problems where the presented high order AMR scheme behaves
clearly better than traditional second order AMR methods. The proposed scheme
that combines for the first time high order ADER methods with space--time
adaptive grids in two and three space dimensions is likely to become a useful
tool in several fields of computational physics, applied mathematics and
mechanics.Comment: With updated bibliography informatio
Reducing numerical diffusion in magnetospheric simulations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95441/1/jgra21205.pd
Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers
In this paper we use the genuinely multidimensional HLL Riemann solvers
recently developed by Balsara et al. to construct a new class of
computationally efficient high order Lagrangian ADER-WENO one-step ALE finite
volume schemes on unstructured triangular meshes. A nonlinear WENO
reconstruction operator allows the algorithm to achieve high order of accuracy
in space, while high order of accuracy in time is obtained by the use of an
ADER time-stepping technique based on a local space-time Galerkin predictor.
The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the
grid, considering the entire Voronoi neighborhood of each node and allows for
larger time steps than conventional one-dimensional Riemann solvers. The
results produced by the multidimensional Riemann solver are then used twice in
our one-step ALE algorithm: first, as a node solver that assigns a unique
velocity vector to each vertex, in order to preserve the continuity of the
computational mesh; second, as a building block for genuinely multidimensional
numerical flux evaluation that allows the scheme to run with larger time steps
compared to conventional finite volume schemes that use classical
one-dimensional Riemann solvers in normal direction. A rezoning step may be
necessary in order to overcome element overlapping or crossing-over. We apply
the method presented in this article to two systems of hyperbolic conservation
laws, namely the Euler equations of compressible gas dynamics and the equations
of ideal classical magneto-hydrodynamics (MHD). Convergence studies up to
fourth order of accuracy in space and time have been carried out. Several
numerical test problems have been solved to validate the new approach
Simulating radiative shocks in nozzle shock tubes
We use the recently developed Center for Radiative Shock Hydrodynamics
(CRASH) code to numerically simulate laser-driven radiative shock experiments.
These shocks are launched by an ablated beryllium disk and are driven down
xenon-filled plastic tubes. The simulations are initialized by the
two-dimensional version of the Lagrangian Hyades code which is used to evaluate
the laser energy deposition during the first 1.1ns. The later times are
calculated with the CRASH code. This code solves for the multi-material
hydrodynamics with separate electron and ion temperatures on an Eulerian
block-adaptive-mesh and includes a multi-group flux-limited radiation diffusion
and electron thermal heat conduction. The goal of the present paper is to
demonstrate the capability to simulate radiative shocks of essentially
three-dimensional experimental configurations, such as circular and elliptical
nozzles. We show that the compound shock structure of the primary and wall
shock is captured and verify that the shock properties are consistent with
order-of-magnitude estimates. The produced synthetic radiographs can be used
for comparison with future nozzle experiments at high-energy-density laser
facilities.Comment: submitted to High Energy Density Physic
- …