an:07302210
Zbl 1453.65245
Danilov, S.; Kutsenko, A.
On the geometric origin of spurious waves in finite-volume discretizations of shallow water equations on triangular meshes
EN
J. Comput. Phys. 398, Article ID 108891, 19 p. (2019).
00457911
2019
j
65M08 86A05 86A10 65Z05
triangular meshes; finite volume discretization; computational dispersion branches
Summary: Computational wave branches are common to linearized shallow water equations discretized on triangular meshes. It is demonstrated that for standard finite-volume discretizations these branches can be traced back to the structure of the unit cell of triangular lattice, which includes two triangles with a common edge. Only subsets of similarly oriented triangles or edges possess the translational symmetry of unit cell. As a consequence, discrete degrees of freedom placed on triangles or edges are geometrically different, creating an internal structure inside unit cells. It implies a possibility of oscillations inside unit cells seen as computational branches in the framework of linearized shallow water equations, or as grid-scale noise generally. Adding dissipative operators based on smallest stencils to discretized equations is needed to control these oscillations in solutions. A review of several finite-volume discretization is presented with focus on computational branches and dissipative operators.