TABLE OF CONTENTS / Initial Conditions / Mesh Generation for SPAM with Free Boundaries / Fixed Boundaries / Free Boundaries / Implementing Periodic and Mirror Boundaries / Alternative Meshes Regular Lattices / Elastic Stability of Embedded-Atom Lattices / Crystal Stabilization via Invariant Curvature /
/ 12 Figures /
Example Problems :
[ Elastic Stability of a Triangular Lattice Fluid, One-Dimensional Heat Transfer, Periodic Shear Flow, Rayleigh-B nard Flow ]
All the types of time-dependent simulation algorithms, Eulerian, La-grangian, and SPAM, have common features. To begin with, all these simulations require initial conditions. At least coordinates and velocities are required; often additional variables such as energy, stress, or elastic and plastic strains must be specified too. To continue, motion equations are required for the variables' evolution, as well as constitutive relations and boundary conditions. Last, a compatible time integration algorithm needs to be developed and implemented.
For simulations which are expected to reach a stationary state the initial conditions are typically guessed on the basis of simple physical principles. Consider the two-roll Rayleigh-B nard problem of Section 2.12 . One way to start out is to choose the simplest nonvanishing Fourier components consistent with the boundary conditions on the flow. We will treat that same flow in this Chapter, as an example problem with SPAM. With grid-based simulation methods the choice of mesh is a relatively straightforward, but tedious chore. A finite-element mesh for an automobile can require months to construct.
SPAM is quite different to the usual finite-element approaches, in that the...
