The authors construct summation-by-parts based schemes for the Serre-Green-Naghdi equations in both standard and hyperbolic forms that conserve mass and energy, are well-balanced, and demonstrate improved accuracy for dispersive waves on coarse meshes.
Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate.ACM Transactions on Math- ematical Software (TOMS), 35(3):1–14
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Structure-preserving approximations of the Serre-Green-Naghdi equations in standard and hyperbolic form
The authors construct summation-by-parts based schemes for the Serre-Green-Naghdi equations in both standard and hyperbolic forms that conserve mass and energy, are well-balanced, and demonstrate improved accuracy for dispersive waves on coarse meshes.