Computer Simulation of Dynamic Phenomena

ISBN-13: 9783540630708 / Angielski / Twarda / 1999 / 246 str.

Mark L. Wilkins; M. L. Wilkins; R. Glowinski

Opis

This text describes computer programs for simulating phenomena in hydro- dynamics, gas dynamics, and elastic plastic flow in one, two, and three dimen- sions. Included in the two-dimensional program are Maxwell's equations and thermal and radiation diffusion. The programs were developed by the author during the years 1952-1985 at the Lawrence Livermore National Laboratory. The largest main-frame computers available in the early 1950s were re- quired to solve hydrodynamic problems in one space dimension by using forty mass points. Subsequently, numerical methods were developed for solv- ing problems in two and three space dimensions, but application of these methods had to wait until the main-frame computers were large enough to tackle meaningful problems. At the present time, lap-top computers can use these methods to solve problems in three space dimensions with the detail of 10 000 mass points. The numerical procedures described in the text permit the exact con- servation of physical properties in the solutions of the fundamental laws of mechanics: (1) conservation of mass, (2) conservation of momentum, (3) con- servation of energy. The laws of mechanics are universal in their application. Examples are given for the same computer simulation programs solving prob- lems of penetration mechanics, surface waves from earthquakes, shock waves in solids and gases, failure of materials.

Recenzje

From the reviews
"The focus on the numerical scheme by the author was particularly good. Text, equations and illustrations have been employed very well to explain the methods of producing the numerical code. The procedure to implement them practically is also well documented." (The Physicist, 2000)

"(....) the book offers a unique and interesting blend of numerical fluid and solid mechanics. As such, it should serve well as a reference for a graduate course on computational mechanics." (Applied Mechanics Reviews, 1999)

Spis treści

1. Elements of Fluid Mechanics.- 2. Numerical Techniques.- 3. Modeling the Behavior of Materials.- 4. Two-Dimensional Elastic—Plastic Flow.- 5. Sliding Interfaces in Two Dimensions.- 6. Elastic—Plastic Flow in Three Space Dimensions.- 7. Sliding Surfaces in Three Dimensions.- 8. Magnetohydrodynamics of HEMP.- Appendices.- A. Effect of a Second Shock on the Principal Hugoniot.- B. Finite Difference Program for One Space Dimension and Time.- B.1 Fundamental Equations.- B.2 Finite Difference Equations.- B.3 Boundary Conditions.- B.4 Opening and Closing Voids.- C. A Method for Determining the Plastic Work Hardening Function.- C.1 Application to 6061-T6 Aluminum.- D. Detonation of a High Explosive for a ?-Law Equation of State.- E. Magnetic Flux Calculation.- F. Thermal Diffusion Calculation.- References.

Blurb

Preferred finite difference schemes in one, two, and three space dimensions are described for solving the three fundamental equations of mechanics (conservation of mass, conservation of momentum, and conservation of energy). Models of the behavior of materials provide the closure to the three fundamentals equations for applications to problems in compressible fluid flow and solid mechanics. The use of Lagrange coordinates permits the history of mass elements to be followed where the integrated effects of plasticity and external loads change the material physical properties. Models of fracture, including size effects, are described. The detonation of explosives is modelled following the Chapman--Jouget theory with equations of state for the detonation products derived from experiments. An equation-of-state library for solids and explosives is presented with theoretical models that incorporate experimental data from the open literature. The versatility of the simulation programs is demonstrated by applications to the calculations of surface waves from an earthquake to the shock waves from supersonic flow and other examples.