A no-go theorem shows density-independent mass matrices on Delaunay-Voronoi meshes produce an unavoidable O(h²) energy residual in discrete vector-invariant barotropic Navier-Stokes; the density-weighted matrix eliminates the residual and yields global well-posedness plus discrete stability.
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A structure-preserving discretization of incompressible Euler and Navier-Stokes equations using discrete exterior calculus that enforces exact conservation and excludes dissipative weak solutions above the Onsager threshold.
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A no-go theorem and its resolution for the discrete compressible barotropic Navier--Stokes equations
A no-go theorem shows density-independent mass matrices on Delaunay-Voronoi meshes produce an unavoidable O(h²) energy residual in discrete vector-invariant barotropic Navier-Stokes; the density-weighted matrix eliminates the residual and yields global well-posedness plus discrete stability.
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Exact conservation and the Onsager threshold: a discrete exterior calculus theory for incompressible Navier-Stokes Equations
A structure-preserving discretization of incompressible Euler and Navier-Stokes equations using discrete exterior calculus that enforces exact conservation and excludes dissipative weak solutions above the Onsager threshold.