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A method for post-processing the velocity after a pressure projection isdeveloped that helps to maintain stability in an under-resolved, inviscid,discontinuous element-based simulation for use in environmental fluid mechanicsprocess studies. The post-processing method is needed because of spuriousdivergence growth at element interfaces due to the discontinuous nature of thediscretization used. This spurious divergence eventually leads to a numericalinstability. Previous work has shown that a discontinuous element-localprojection onto the space of divergence-free basis functions is capable ofstabilizing the projection method, but the discontinuity inherent in thistechnique may lead to instability in under-resolved simulations. By enforcinginter-element discontinuity and requiring a divergence-free result in the weaksense only, a new post-processing technique is developed that simultaneouslyimproves smoothness and reduces divergence in the pressure-projected velocityfield at the same time. When compared against a non-post-processed velocityfield, the post-processed velocity field remains stable far longer and exhibitsbetter smoothness and conservation properties.

A post-processing technique for stabilizing the discontinuous pressure projection operator in marginally-resolved incompressible inviscid flow