The Calculation of Hydrodynamic Shocks by Numerical Methods - A Tutorial

THE CALCULATION OF HYDRODYNAMIC SHOCKS BY NUMERICAL METHODS: A TUTORIAL Dr. Paul H. Rosenthal, Professor California State University, Los Angeles This paper is an extract of my thesis submitted in partial fulfillment of the requirements for the Master of Arts degree at Temple University, June 1, 1953. It is being published online to honor the memory of Drs. Robert Richtmyer and John Von Neumann whose generous support and advice made it possible. June 1, 1953 INDEX Page I. SHOCK HYDRODYNAMICS 1 1. Introduction 2. Lagrangian and Eularian system 3. Equations of motion 4. Energy equation 5. Properties of shook II. AN ILLUSTRATION; AN ANALYTIC SOLUTION OF A SIMPLE PROBLEM 4 1. A plane piston problem 2. Definition of terms 3. Hugoniot’s equation for shocks 4. Analytic solution of advancing shock front 5. Status of advanced methods of solution III. A COMPLEX HYDRODYNAMICAL PROBEM 9 1. Description 2. Definition of terms 3. Discussion of properties 4. Equations of motion 5. Conservation equations 6. Viscosity method of integration 7. Stability condition IV. SOLUTION BY NUMERICAL METHODS 18 1. Partial difference operator as an approximation to the partial derivative 2. Lagrangian mesh 3. Centering of the difference equations 4. Derivation of the difference equations 5. Form for the .equations of ...