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An accurate finite element method for the numerical solution of isothermal and incompressible flow of viscous fluid, part I: computational analysis. (arXiv:1709.00913v2 [cs.CE] UPDATED)
来源于:arXiv
Despite its numerical challenges, finite element method is used to compute
viscous fluid flow. A consensus on the cause of numerical problems has been
reached; however, general algorithms---allowing a robust and accurate
simulation for any process---are still missing. Either a very high
computational cost is necessary for a direct numerical solution (DNS) or some
limiting procedure is used by adding artificial dissipation to the system.
These stabilization methods are often applied relative to the element size such
that a local monotonous convergence cannot be observed. We need a computational
strategy for solving viscous fluid flow using only the balance equations. In
this work, we present a general procedure solving fluid mechanics problems
without use of any stabilization or splitting schemes. Hence its generalization
to multiphysics applications is straight-forward. We discuss several numerical
problems and present the methodology rigorously. Implementation is achieved by
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