A time-dependent incompressible viscous BEM for moderate Reynolds numbers

The boundary element method is applied to transient viscous incompressible flow. The time-domain formulation allows a boundary-only solution for linear Stokes flow. For higher speed flows in which the nonlinear convective effects cannot be ignored, a volume integral must be retained. However, the introduction of reference velocities often limits the nonlinear region to the vicinity of obstacles or boundary surfaces. Additionally, the volume terms are rewritten to eliminate the need for the calculation of velocity gradients. A general purpose numerical implementation of this new formulation then produces a very attractive tool for engineering analysis. This implementation includes a Newton-Raphson algorithm, permitting accurate solutions up to the moderate Reynolds number range. Several numerical examples are provided to validate the present approach.