Engineering topics

Myhill, Elizabeth A.

Publications and source records attributed to Myhill, Elizabeth A..

3 records

NASA NTRS1993

Protostellar hydrodynamics: Constructing and testing a spacially and temporally second-order accurate method. 2: Cartesian coordinates

In Boss & Myhill (1992) we described the derivation and testing of a spherical coordinate-based scheme for solving the hydrodynamic equations governing the gravitational collapse of nonisothermal, nonmagnetic, inviscid, radiative, three-dimensional protostellar clouds. Here we discuss a Cartesian coordinate-based scheme based on the same set of hydrodynamic equations. As with the spherical coorrdinate-based code, the Cartesian coordinate-based scheme employs explicit Eulerian methods which are both spatially and temporally second-order accurate. We begin by describing the hydrodynamic equations in Cartesian coordinates and the numerical methods used in this particular code. Following Finn & Hawley (1989), we pay special attention to the proper implementations of high-order accuracy, finite difference methods. We evaluate the ability of the Cartesian scheme to handle shock propagation problems, and through convergence testing, we show that the code is indeed second-order accurate. To compare the Cartesian scheme discussed here with the spherical coordinate-based scheme discussed in Boss & Myhill (1992), the two codes are used to calculate the standard isothermal collapse test case described by Bodenheimer & Boss (1981). We find that with the improved codes, the intermediate bar-configuration found previously disappears, and the cloud fragments directly into a binary protostellar system. Finally, we present the results from both codes of a new test for nonisothermal protostellar collapse.

Myhill, Elizabeth A.↗

NASA NTRS1992

Protostellar hydrodynamics: Constructing and testing a spatially and temporally second-order-accurate method. I - Spherical coordinates

Two related numerical schemes for calculating the 3D collapse of protostellar clouds are defined, developed, and checked on a wide variety of test problems in spherical symmetry and multiple dimensions. One scheme is first-order accurate in time (code S), and the other second-order accurate in time (code ST). Through convergence testing, the codes are shown to be second-order accurate in spatial differences. Compared with the previous 3D code, the combination of reduced numerical dissipation through second-order accuracy and of removing the systematic bias toward central concentrations implies that the tendency for fragmentation into binary or multiple protostars should increase. A reinvestigation of fragmentation as a mechanism for forming binary stars is expected to yield an even more favorable evaluation.

Boss, Alan P.↗

NASA NTRS1992

Numerical models for the collapse and fragmentation of centrally condensed molecular cloud cores

The gravitational collapse and fragmentation of centrally condensed molecular cloud cores are investigated using a new hydrodynamical code. The numerical scheme is second-order accurate and uses explicit finite difference methods to advance the fluid variables on a 3D Cartesian grid. Two initial power-law density profiles, rho varies as r exp -1 and rho varies as r exp -2, are considered, as well as two initial density perturbations in the azimuthal coordinate theta, rho-i - rho(1 + a cos 2theta) where a = 0.1 and 0.5. Fragmentation is found to be possible in these centrally condensed cores if the initial conditions also include differential rotation. Models which collapse with initial uniform rotation do not produce fragments. If molecular cloud cores are indeed centrally condensed, as suggested by observations of star-forming regions and by studies of ambipolar diffusion, then differential rotation may be a mechanism for producing binary protostars during gravitational collapse.

Myhill, Elizabeth A.↗