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Error analysis of a SUPG-stabilized POD-ROM method for convection-diffusion-reaction equations
A reduced order model (ROM) method based on proper orthogonal decomposition (POD) is analyzed for convection-diffusion-reaction equations. The streamline-upwind Petrov--Galerkin (SUPG) stabilization is used in the practically interesting case of dominant convection, both for the full order method (FOM) and the ROM simulations. The asymptotic choice of the stabilization parameter for the SUPG-ROM is done as proposed in the literature. This paper presents a finite element convergence analysis of the SUPG-ROM method for errors in different norms. The constants in the error bounds are uniform with respect to small diffusion coefficients. Numerical studies illustrate the performance of the SUPG-ROM method.
On the feasibility of using open source solvers for the simulation of a turbulent air flow in a dairy barn
Two transient open source solvers, OpenFOAM and ParMooN, are assessed with respect to the simulation of the turbulent air flow inside and around a dairy barn. For this purpose, data were obtained in an experimental campaign at a 1:100 scaled wind tunnel model. Both solvers used different meshes, discretization schemes, and turbulence models. The experimental data and numerical results agree well for time-averaged stream-wise and vertical-wise velocities. In particular, the air exchange was predicted with high accuracy by both solvers with relative errors less than 5 % compared to the experimental results. With respect to the turbulent quantities, good agreements at the second (downwind) half of the barn inside and especially outside the barn could be achieved, where both codes accurately predicted the flow separation and the root-mean-square velocities. Deviations between simulations and experimental results regarding turbulent quantities could be observed in the first part of the barn, due to different inlet conditions between the experimental setup and the numerical simulations. Both solvers proved to be promising tools for the accurate prediction of time-dependent phenomena in an agricultural context, e.g., like the transport of particulate matter or pathogen-laden aerosols in and around agricultural buildings.