Weston Lowrie

A priori mesh quality metric error analysis applied to a high-order finite element method

Characterization of computational meshs quality prior to performing a numerical simulation is an important step in insuring that the result is valid. A highly distorted mesh can result in significant errors. It is therefore desirable to predict solution accuracy on a given mesh. The HiFi/SEL high-order finite element code is used to study the effects of various mesh distortions on solution quality of known analytic problems for spatial discretizations with different order of finite elements. The measured global error norms are compared to several mesh quality metrics by independently varying both the degree of the distortions and the order of the finite elements. It is found that the spatial spectral convergence rates are preserved for all considered distortion types, while the total error increases with the degree of distortion. For each distortion type, correlations between the measured solution error and the different mesh metrics are quantified, identifying the most appropriate overall mesh metric. The results show promise for future a priori computational mesh quality determination and improvement.

The Sheared-Flow Stabilized Z-Pinch

The stabilizing effect of a sheared axial flow is investigated in the ZaP Flow Z-pinch experiment at the University of Washington. Long-lived, Z-pinch plasmas are generated that are 100 cm long with a 1 cm radius and exhibit gross stability for many Alfvén transit times. Experimental measurements show a sheared flow profile that is coincident with the quiescent period during which magnetic fluctuations are diminished. The flow shear is generated with flow speeds less than the Alfvén speed. While the electrodes contact the ends of the Z-pinch, the surrounding wall is far enough from the plasma that the wall does not affect stability, as is investigated experimentally and computationally. Relations are derived for scaling the plasma to high energy density and to a fusion reactor. The sheared flow stabilized Z-pinch concept provides a compact linear system.

Effects of a Conducting Wall on Z-Pinch Stability

The stabilizing effect of a conducting wall on Z-pinch stability has been investigated through a systematic experimental and numerical study. Numerical simulations of a Z-pinch with a cylindrical conducting wall are compared with a case that modeled perforations in the conducting wall. The conducting wall also acts as the return current path for these investigations. Plasma conditions with various pinch sizes were studied numerically to better understand the effect of wall stabilization in Z-pinches. A study using the ZaP Flow Z-Pinch was performed by inserting a 0.35-m perforated section of electrode that has eight longitudinal slots cut from the outer electrode, reducing the conducting wall material by ≈70% .This modification prevents currents from flowing freely along the azimuthal distance of the outer electrode required to stabilize the m = 1, 2, 3 modes, which are experimentally monitored. Operating with identical experimental parameters with and without the perforated electrode was assumed to produce similar equilibrium and flow shear conditions in the pinch. Comparing the stability characteristics isolated the potential effects of the conducting wall. Magnetic data, interferometry, and optical images indicate that the conducting wall does not have a discernible effect on stability in the ZaP experiment. This result agrees with simulations with similar ratios of conducting wall radius to pinch radius.

High energy density Z-pinch plasmas using flow stabilization

The ZaP Flow Z-Pinch research project[1] at the University of Washington investigates the effect of sheared flows on MHD instabilities. Axially flowing Z-pinch plasmas are produced that are 100 cm long with a 1 cm radius. The plasma remains quiescent for many radial Alfven times and axial flow times. The quiescent periods are characterized by low magnetic mode activity measured at several locations along the plasma column and by stationary visible plasma emission. Plasma evolution is modeled with high-resolution simulation codes – Mach2, WARPX, NIMROD, and HiFi. Plasma flow profiles are experimentally measured with a multi-chord ion Doppler spectrometer. A sheared flow profile is observed to be coincident with the quiescent period, and is consistent with classical plasma viscosity. Equilibrium is determined by diagnostic measurements: interferometry for density; spectroscopy for ion temperature, plasma flow, and density[2]; Thomson scattering for electron temperature; Zeeman splitting for internal magneti...