A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method [M. S. Mohamed, A. N. Hirani, and R. Samtaney, "Discrete exterior calculus discretization of incompressible Navier-Stokes equations over surface simplicial meshes," J. Comput. Phys. 312, 175-191 (2016)] is modified to this end and is extended to include the energy-preserving time integration and the Coriolis force to enhance its applicability to investigate the late-time behavior of flows on rotating surfaces, i.e., that of the planetary flows. The simulation experiments show second order accuracy of the scheme for the structured-triangular meshes and first order accuracy for the otherwise unstructured meshes. The method exhibits a second order kinetic energy relative error convergence rate with mesh size for inviscid flows. The test case of flow on a rotating sphere demonstrates that the method preserves the stationary state and conserves the inviscid invariants over an extended period of time.

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In the present work, numerical simulations have been performed on a model problem, representing a class of fluid-structure interaction problems. The model problem consists of a thin plate with a flow channel embedded in it. The governing equations for flow in the channel and displacement in plate structure are discretized using a finite volume procedure on unstructured meshes, and are solved in a one-way coupled manner with the flow in the channel influencing the stress field in the structure. The problem is presented in a generalized manner, in terms of the relevant dimensionless parameters obtained as part of the analysis. A parametric study is performed for the cases of isothermal and with heating of the fluid. The data from the parametric simulations are used to explain the stress field behavior in the solid plate, in response to independent dimensionless parameters. The overall methodology is presented in a manner that will be useful in analyzing any specific case of the class of fluid-structure interaction represented by the model problem.

A unified cell-centered unstructured mesh finite volume procedure is presented for fluid flow, heat transfer and solid-body stress analysis. An in-house procedure (A. W. Date, Solution of Transport Equations on Unstructured Meshes with Cell-Centered Colocated Variables.

The giant vortex in Jupiter's atmosphere, the great red spot (GRS), has grabbed attention of not only astrophysicists but also of fluid dynamists. What fluid dynamics/thermodynamics conditions might have formed it and made it extremely stable and long-lived are some fundamental questions of interest, and the present work addresses these. We model the GRS numerically using a structure-preserving Discrete Exterior Calculus (DEC) method. Our initial condition comprises of vortices embedded in a shearing zonal flow. We solve the continuity and momentum equation (that conserves the potential vorticity) on a sphere (thereby including sphericity and excluding domain boundary influence), for incompressible, inviscid flow with uniform fluid properties. We investigate the vorticity dynamics of vortices in shearing zonal flows for a range of parameters. Our simulations show evolution of a stable vortex in a zonal band similar to the GRS.