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**Conservation properties of unstructured staggered mesh schemes.**
*(English)*
Zbl 0972.76068

From the summary: This work addresses the momentum, kinetic energy, and circulation conservation properties of unstructured staggered mesh methods. It is shown that with certain choices of the velocity interpolation, unstructured staggered mesh discretizations of the divergence form of the Navier-Stokes equations can conserve kinetic energy and momentum both locally and globally. In addition, it is shown that unstructured staggered mesh discretizations of the rotational form of the Navier-Stokes equations can conserve kinetic energy and circulation both locally and globally. The analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation. It is shown that the methods are first-order accurate on nonuniform two-dimensional unstructured meshes and second-order accurate on uniform unstructured meshes. We also present numerical confirmation of the conservation properties and of the order of accuracy of these unstructured staggered mesh methods.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76D05 | Navier-Stokes equations for incompressible viscous fluids |

### Keywords:

accuracy; conservation properties; unstructured staggered mesh methods; Navier-Stokes equations; kinetic energy; momentum### References:

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