Abstract
Smoothed particle hydrodynamics (SPH) is being used to model fluid flows, including free surface waves; however, the method assumes an compressible fluid. Most water wave theories are based on the assumption of incompressibility, which is reasonable for water. Here we develop a linear wave theory for waves on a compressible fluid. The effect of the fluid compressibility on wave number is examined to determine how much error is induced by an assumption of compressibility and also how these effects might be avoided. The dispersion relationship for a free surface wave on a compressible fluid is determined and the results are compared to incompressible free surface wave theory. ?? 2007 World Scientific Publishing Co. Pte. Ltd.
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