We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe non-hydrostatic atmospheric flow. The well-balancing of the approach is ensured by a local hydrostatic reconstruction updated in runtime during the simulation to keep the numerical error under control. To approximate the solution of the Riemann problem, we consider four methods: Roe-Pike, HLLC, AUSM+-up and HLLC-AUSM. We assess our density-based approach and compare the accuracy of these four approximated Riemann solvers using two classical benchmarks, namely the smooth rising thermal bubble and the density current.
Computational study of numerical flux schemes for mesoscale atmospheric flows in a Finite Volume framework / Clinco, Nicola; Girfoglio, Michele; Quaini, Annalisa; Rozza, Gianluigi. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 15:1(2024), pp. 106-122. [10.2478/caim-2024-0017]
Computational study of numerical flux schemes for mesoscale atmospheric flows in a Finite Volume framework
Clinco, Nicola;Girfoglio, Michele;Quaini, Annalisa;Rozza, Gianluigi
2024-01-01
Abstract
We develop, and implement in a Finite Volume environment, a density-based approach for the Euler equations written in conservative form using density, momentum, and total energy as variables. Under simplifying assumptions, these equations are used to describe non-hydrostatic atmospheric flow. The well-balancing of the approach is ensured by a local hydrostatic reconstruction updated in runtime during the simulation to keep the numerical error under control. To approximate the solution of the Riemann problem, we consider four methods: Roe-Pike, HLLC, AUSM+-up and HLLC-AUSM. We assess our density-based approach and compare the accuracy of these four approximated Riemann solvers using two classical benchmarks, namely the smooth rising thermal bubble and the density current.File | Dimensione | Formato | |
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