2018
DOI: 10.1002/fld.4510
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Abstract: Summary Stationary and instationary Stokes and Navier‐Stokes flows are considered on two‐dimensional manifolds, ie, on curved surfaces in three dimensions. The higher‐order surface FEM is used for the approximation of the geometry, velocities, pressure, and Lagrange multiplier to enforce tangential velocities. Individual element orders are employed for these various fields. Streamline‐upwind stabilization is employed for flows at high Reynolds numbers. Applications are presented, which extend classical benchma… Show more

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Cited by 61 publications
(98 citation statements)
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“…2(e) shows the resulting flow field for an instationary Navier-Stokes flow and the resulting Kármán vortex street can clearly be seen. The test cases are documented in detail in [4,5].…”
Section: Numerical Resultsmentioning
confidence: 99%
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“…2(e) shows the resulting flow field for an instationary Navier-Stokes flow and the resulting Kármán vortex street can clearly be seen. The test cases are documented in detail in [4,5].…”
Section: Numerical Resultsmentioning
confidence: 99%
“…The boundary conditions extend in time and a divergence-free, tangential, initial condition for u is needed. The (stabilized) weak forms of the governing equations are found in [4,5] and are omitted here for brevity. The surface FEM [6] is used for the discretization.…”
Section: Governing Equationsmentioning
confidence: 99%
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“…[7][8][9][10] Surface convection and diffusion problems are also fundamental subproblems involved in the surface flow models with applications to geoscience. [11][12][13][14][15][16] While there are a lot of discussions on numerical methods in the literature for convection-diffusion-reaction PDEs in one, two, and three dimensions, it is challenging to develop efficient numerical methods for such PDEs on surfaces (or manifolds).…”
Section: Introductionmentioning
confidence: 99%
“…The P 2 -P 1 continuous Taylor-Hood element is one of the most popular FE pairs for incompressible fluid flow problems. Surface variants of this pair have been used for surface Navier-Stokes equations in the recent papers [35,12]. In those papers the fitted surface FE approach is used.…”
mentioning
confidence: 99%