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Advisory Committee Chair

Dr David L Littlefield

Advisory Committee Members

Dr Dean L Sicking

Dr Lee G Lee

Document Type

Thesis

Date of Award

2019

Degree Name by School

Master of Science in Mechanical Engineering (MSME) School of Engineering

Abstract

In this study, we examine a number of approximations in the formulation of hydrocodes. These approximations were borne out of an original requirement for the code to run as fast as possible i.e. with accuracy being secondary to speed. Many of these approximations originated from the 1970’s when computers were slow and memory was at a premium. Although speed and memory are not as much of an issue today, these approximations are still used to formulate the hydrocodes. In this study, the effect of these approximations is examined systematically. The lumped mass approximation is a simplification to the consistent mass formulation and is routinely used in hydrocodes. While this approximation is computationally efficient, the consistent mass formulation is the most accurate (and computationally expensive) option. There are other levels of approximation between these two extremes that trade off computational efficiency for accuracy. As is shown in this work, some of these result in tridiagonal systems which are very computationally efficient to solve. We introduce these algorithms in this work and refer to them as the reduced consistent mass method. Linear finite elements are also used pervasively in hydrocodes. Like the lumped mass approximation, the use of linear elements was borne out of the requirement for computational efficiency and not accuracy. Surprisingly, linear elements are still used routinely today, despite their numerous accuracy issues such as realistic representation of geometry and the need for hourglass stabilization. In this work higher order finite elements, including quadratic and cubic elements, are examined. Special attention is placed on quadrature order used in integration and its effect on overall accuracy. The 2D version of ALEAS (Arbitrary Lagrangian-Eulerian Adaptive Solver), an in-house ALE (Arbitrary Lagrangian-Eulerian) research code, is used in this work. Some simple benchmark problems are used to assess and quantify the effect of higher order approximations in Eulerian hydrocodes.

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