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In the absence of important atomic-scale effects, macroscopic continuum mechanics is the method of choice for simulation. In continuum mechanics the density, velocity, pressure, and similar field variables are assumed to vary continuously throughout the space-time region of interest. Undergraduate texts describe the solution of "easy" continuum problems, including the flow of heat in response to imposed thermal boundary conditions and the linear-elastic response of solids to imposed loads. A variety of grid-based approaches work very well for such problems. For more difficult problems, in which the structure under study undergoes extreme shape changes and forms new surfaces while resisting interpenetration at interfaces, more sophisticated and flexible techniques are required.

C. G. Hoover and W. G. Hoover, "SPAM-Based Recipes for Continuum Simulations," in Computing in Science & Engineering, vol. 3, no. , pp. 78-85, 2001.
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