CFD simulations promise to make great contributions to understand the airflow characteristics of healthy and pathologic noses. Before surgery, planning for any specific intervention using CFD techniques on the nasal cavity model of the patient may help foreseeing the aerodynamic effects of the operation and might increase the success rate of the surgical treatment.

Numerical simulations of laminar, forced convection heat transfer for reciprocating, two-dimensional channel flows are performed as a function of the penetration length, Womersley (α) and Prandtl (Pr) numbers. The numerical algorithm is based on a spectral element formulation, which enables high-order spatial resolution with exponential decay of discretization errors, and second-order time-accuracy. Uniform heat flux and constant temperature boundary conditions are imposed on certain regions of the top surface, while the bottom surface is kept insulated. Periodicity of velocity and temperature fields is imposed on the side boundaries, while the flow is driven by an oscillating pressure gradient. These sets of boundary conditions enable time-periodic solution of the problem. Instantaneous and time-averaged surface and bulk temperature distributions, and Nusselt number variations are presented. For high α flows, the temperature field is significantly affected by the Richardson’s annular effect. Overall, forced convection increases by increasing the penetration length, α and Pr. Corresponding steady-flow simulations are performed by matching the volumetric flowrate. For the limited parameter space investigated in this paper, steady unidirectional forced convection is more effective than the reciprocating flow forced convection.

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Purpose This study aims to focus on the development of a high-order discontinuous Galerkin method for the solution of unsteady, incompressible, multiphase flows with level set interface formulation. Design/methodology/approach Nodal discontinuous Galerkin discretization is used for incompressible Navier–Stokes, level set advection and reinitialization equations on adaptive unstructured elements. Implicit systems arising from the semi-explicit time discretization of the flow equations are solved with a p-multigrid preconditioned conjugate gradient method, which minimizes the memory requirements and increases overall run-time performance. Computations are localized mostly near the interface location to reduce computational cost without sacrificing the accuracy. Findings The proposed method allows to capture interface topology accurately in simulating wide range of flow regimes with high density/viscosity ratios and offers good mass conservation even in relatively coarse grids, while keeping the simplicity of the level set interface modeling. Efficiency, local high-order accuracy and mass conservation of the method are confirmed through distinct numerical test cases of sloshing, dam break and Rayleigh–Taylor instability. Originality/value A fully discontinuous Galerkin, high-order, adaptive method on unstructured grids is introduced where flow and interface equations are solved in discontinuous space.

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