Optimal multistage schemes for Euler equations with residual smoothing

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76583/1/AIAA-12860-858.pd

Analysis and Implementation of Recovery-Based Discontinuous Galerkin for Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76575/1/AIAA-2009-3786-303.pd

Effect of Expansion and Magnetic Field Configuration on Mass Entrainment of Jets

We investigate the growth of jet plus entrained mass in simulations of supermagnetosonic cylindrical and expanding jets. The entrained mass spatially grows in three stages: from an initially slow spatial rate to a faster rate and finally at a flatter rate. These stages roughly coincide with the similar rates of expansion in simulated radio intensity maps, and also appear related to the growth of the Kelvin-Helmholtz instability through linear, nonlinear, and saturated regimes. In the supermagnetosonic cylindrical jets, we found that a jet with an embedded primarily toroidal magnetic field is more stable than a jet with a primarily axial magnetic field. Also, pressure-matched expanding jets are more stable and entrain less mass than cylindrical jets with equivalent inlet conditions.Comment: to appear in Life Cycles of Radio Galaxies, ed. J. Biretta et al., New Astronomy Reviews; 6 pages, including 3 figure

A Simple and Accurate Riemann Solver for Isothermal MHD

A new approximate Riemann solver for the equations of magnetohydrodynamics (MHD) with an isothermal equation of state is presented. The proposed method of solution draws on the recent work of Miyoshi and Kusano, in the context of adiabatic MHD, where an approximate solution to the Riemann problem is sought in terms of an average constant velocity and total pressure across the Riemann fan. This allows the formation of four intermediate states enclosed by two outermost fast discontinuities and separated by two rotational waves and an entropy mode. In the present work, a corresponding derivation for the isothermal MHD equations is presented. It is found that the absence of the entropy mode leads to a different formulation which is based on a three-state representation rather than four. Numerical tests in one and two dimensions demonstrates that the new solver is robust and comparable in accuracy to the more expensive linearized solver of Roe, although considerably faster.Comment: 19 pages, 9 figure

Solving One Dimensional Scalar Conservation Laws by Particle Management

We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle management. Since no global remeshing is required, shocks stay sharp and propagate at the correct speed, while rarefaction waves are created where appropriate. The method is TVD, entropy decreasing, exactly conservative, and has no numerical dissipation. Difficulties involving transonic points do not occur, however inflection points of the flux function pose a slight challenge, which can be overcome by a special treatment. Away from shocks the method is second order accurate, while shocks are resolved with first order accuracy. A postprocessing step can recover the second order accuracy. The method is compared to CLAWPACK in test cases and is found to yield an increase in accuracy for comparable resolutions.Comment: 15 pages, 6 figures. Submitted to proceedings of the Fourth International Workshop Meshfree Methods for Partial Differential Equation

Efficient multi-stage time marching for viscous flows via local preconditioning

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/77354/1/AIAA-1999-3267-892.pd

Excellent Rings with Singleton Formal Fibers

In this paper we construct a non complete excellent local ring A such that the natural map Spec  → Spec A is bijective

It's a wonderful tail: the mass loss history of Mira

Recent observations of the Mira AB binary system have revealed a surrounding arc-like structure and a stream of material stretching 2 degrees away in opposition to the arc. The alignment of the proper motion vector and the arc-like structure shows the structures to be a bow shock and accompanying tail. We have successfully hydrodynamically modelled the bow shock and tail as the interaction between the asymptotic giant branch (AGB) wind launched from Mira A and the surrounding interstellar medium. Our simulations show that the wake behind the bow shock is turbulent: this forms periodic density variations in the tail similar to those observed. We investigate the possiblity of mass-loss variations, but find that these have limited effect on the tail structure. The tail is estimated to be approximately 450,000 years old, and is moving with a velocity close to that of Mira itself. We suggest that the duration of the high mass-loss phase on the AGB may have been underestimated. Finally, both the tail curvature and the rebrightening at large distance can be qualitatively understood if Mira recently entered the Local Bubble. This is estimated to have occured 17 pc downstream from its current location.Comment: 12 pages, 3 colour figures, accepted by ApJ Part II (Letters

An Unstaggered Constrained Transport Method for the 3D Ideal Magnetohydrodynamic Equations

Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with nonlinear numerical instabilities. One approach for controlling the discrete divergence is through a so-called constrained transport method, which is based on first predicting a magnetic field through a standard finite volume solver, and then correcting this field through the appropriate use of a magnetic vector potential. In this work we develop a constrained transport method for the 3D ideal MHD equations that is based on a high-resolution wave propagation scheme. Our proposed scheme is the 3D extension of the 2D scheme developed by Rossmanith [SIAM J. Sci. Comp. 28, 1766 (2006)], and is based on the high-resolution wave propagation method of Langseth and LeVeque [J. Comp. Phys. 165, 126 (2000)]. In particular, in our extension we take great care to maintain the three most important properties of the 2D scheme: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as cell-centered; (2) we develop a high-resolution wave propagation scheme for evolving the magnetic potential; and (3) we develop a wave limiting approach that is applied during the vector potential evolution, which controls unphysical oscillations in the magnetic field. One of the key numerical difficulties that is novel to 3D is that the transport equation that must be solved for the magnetic vector potential is only weakly hyperbolic. In presenting our numerical algorithm we describe how to numerically handle this problem of weak hyperbolicity, as well as how to choose an appropriate gauge condition. The resulting scheme is applied to several numerical test cases.Comment: 46 pages, 12 figure