TITLE:

Non-Spherical Models of Compact Stellar Objects. (Omair Zubairi)

A High-Order Dirac-Delta Regularization with Optimal Scaling in the Spectral Solution of One-Dimensional Singular Hyperbolic Conservation Laws. (Jean Suarez)

DATE:

Friday, September 19th, 2014

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Jean P Suarez and Omair Zubairi. San Diego State University

ABSTRACT:

Conventionally, the structure of compact stellar objects such as neutron

or quark stars are modeled with the assumption that they are perfect

spheres. However, due to high magnetic fields, certain classes of these

compact stars (such as magnetars and neutron stars containing cores of

color-superconducting quark matter) are expected to be deformed

(non-spherical) making them ob-longed spheroids. In this work, we seek to

investigate the stellar properties of these deformed compact stars in the

framework of general relativity. Using a metric that describes a

non-spherical mass distribution, we derive the stellar structure equations

of these non-spherical compact objects. We then calculate stellar

properties such as mass and radii along with pressure and density profiles

and investigate any changes from the standard spherical models. (Omair Zubairi)

The physics in a range of engineering problems are governed by hyperbolic conservation laws with singular, Dirac delta sources, such as interfaces in multi-phase flows and plasmas and jams in traffic flow. In numerical approximations of these models, the singular sources require regularization. In this talk, we discuss the development of a higher-order resolution regularization technique that suppresses Gibb’s oscillation near singularities, while providing higher-order resolution in region away from the regularization zone. We present a theorethical criterion that determines an optimal scaling of the regularization zone while ensuring a formal order of convergence of the numerical scheme. We validate the theorem with numerical tests including a moving wave described by a linear and nonlinear (Burgers) scalar advection equation with a singular source using spectral methods; as well as, a shock-particle interaction problem described by the nonlinear Euler equations with singular sources (system of hyperbolic conservation laws governing compressible fluid dynamics) using a high-order high-resolution multi-domain hybrid WENO-spectral scheme.

(Jean Suarez)

HOST:

Dr. Jose Castillo

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