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Flow converges to a steady state corresponding to a Killing vector field, from initial velocity profile: $u = (10\cos(2x)\sin(2y),\, 10\sin(xy))$ and $u = (\sin x\cos y,\, \cos(xy))$, respectively.
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The first ten eigenvector fileds of the modified Hodge Laplacian $(\Delta u)^k = g^{ij}u^k_{;ij} + R^k_ju^j$ on a sphere and torus.
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Surface flow around a cylinder.
