Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids

Re, Barbara; Dobrzynski, Cécile; Guardone, Alberto

doi:10.1016/j.amc.2017.03.049

Cited by 11 publications

(8 citation statements)

References 46 publications

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“…There is a vast literature on the topic, and it would be impossible to give a complete overview here. Concerning staggered and cell-centered Lagrangian finite volume schemes on moving meshes, we refer the reader to [119,77,80,76,87,88,84,86,85,82,11,6,12,19,81,112,21,61,62] and references therein. Concerning high order purely Lagrangian DG schemes, see the methods forwarded in [55,56,79].…”

Section: Introductionmentioning

confidence: 99%

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

et al. 2020

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In this paper we propose a new diffuse interface model for the numerical simulation of inviscid compressible flows around fixed and moving solid bodies of arbitrary shape. The solids are assumed to be moving rigid bodies, without any elastic properties. The mathematical model is a simplified case of the seven-equation Baer-Nunziato model of compressible multi-phase flows. The resulting governing PDE system is a nonlinear system of hyperbolic conservation laws with non-conservative products. The geometry of the solid bodies is simply specified via a scalar field that represents the volume fraction of the fluid present in each control volume. This allows the discretization of arbitrarily complex geometries on simple uniform or adaptive Cartesian meshes. Inside the solid bodies, the fluid volume fraction is zero, while it is unitary inside the fluid phase. Due to the diffuse interface nature of the model, the volume fraction function can assume any value between zero and one in mixed cells that are occupied by both, fluid and solid.We also prove that at the material interface, i.e. where the volume fraction jumps from unity to zero, the normal component of the fluid velocity assumes the value of the normal component of the solid velocity. This result can be directly derived from the governing equations, either via Riemann invariants or from the generalized Rankine Hugoniot conditions according to the theory of Dal Maso, Le Floch and Murat [89], which justifies the use of a path-conservative approach for treating the non-conservative products.The governing partial differential equations of our new model are solved on simple uniform Cartesian grids via a high order path-conservative ADER discontinuous Galerkin (DG) finite element method with a posteriori sub-cell finite volume (FV) limiter. Since the numerical method is of the shock capturing type, the fluid-solid boundary is never explicitly tracked by the numerical method, neither via interface reconstruction, nor via mesh motion.The effectiveness of the proposed approach is tested on a set of different numerical test problems, including 1D Riemann problems as well as supersonic flows over fixed and moving rigid bodies.Key words: diffuse interface model, compressible flows over fixed and moving solids, immersed boundary method for compressible flows, arbitrary high-order discontinuous Galerkin schemes, a posteriori sub-cell finite volume limiter (MOOD), path-conservative schemes for hyperbolic PDE with non-conservative products,

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Section: Introductionmentioning

confidence: 99%

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

et al. 2020

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“…This section presents the first validation of the proposed unsteady method for 2D and 3D problems in the NICFD regime. For the validation of the steady version, the reader is referred to [49]. The geometries of the test cases consist in a simple symmetric wedge in 2D and in a portion of a cone in 3D, exposed to a free stream.…”

Section: Assessment Of the Unsteady Adaptive Methods For In Nicfd Regimementioning

confidence: 99%

“…As in the reference, we adopt the polytropic van der Waals model. Further information about the implementation of this thermodynamic model in the flow solver can be found in [49]. The domain extends from x = 0 to x = 1.7 and from y = −0.6 to y = 0.6 (assuming a unitary dimensional reference length of 1 m).…”

Section: Assessment Of the Unsteady Adaptive Methods For In Nicfd Regimementioning

confidence: 99%

“…It appears evident that an effective error indicator will be extremely advantageous to the entire adaptation process. In the NICFD regime, the error estimators based on the Mach number seem to be more efficient than the density-based ones because of the nonmonotone dependence of the Mach number on density along isentropic expansions for supersonic flows at Γ < 1 [49].…”

Section: Adaptation On Flow Featuresmentioning

confidence: 99%

“…To authors' knowledge, this is the first application of unsteady mesh adaptation strategies to NICFD problems, and the interpolation-free approach here exploited represents an added value with respect to standard adaptation techniques in this peculiar thermodynamic regime. This work draws on the investigation of mesh adaptation criteria based on flow variables in the NICFD regime for bi-dimensional steady simulations described in [49].…”

Section: Introductionmentioning

confidence: 99%

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An adaptive ALE scheme for non-ideal compressible fluid dynamics over dynamic unstructured meshes

Guardone

2018

Shock Waves

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This paper investigates the application of mesh adaptation techniques in the Non-Ideal Compressible Fluid Dynamic (NICFD) regime, a region near the vapor-liquid saturation curve where the flow behavior significantly departs from the ideal gas model, as indicated by a value of the fundamental derivative of gasdynamics less than one. A recent interpolation-free finite-volume adaptive scheme is exploited to modify the grid connectivity in a conservative way, and the governing equations for compressible inviscid flows are solved within the Arbitrary Lagrangian Eulerian framework by including special fictitious fluxes representing volume modifications due to mesh adaptation. The absence of interpolation of the solution to the new grid prevents spurious oscillations that may make the solution of the flow field in the NICFD regime more difficult and less robust. Non-ideal gas effects are taken into account by adopting the polytropic Peng-Robinson thermodynamic model. The numerical results focus on the problem of a piston moving in a tube filled with siloxane MD 4 M, a simple configuration which can be the core of experimental research activities aiming at investigating the thermodynamic behavior of NICFD flows. Several numerical tests involving different piston movements and initial states in 2D and 3D assess the capability of the proposed adaption technique to correctly capture compression and expansion waves, as well as the generation and propagation of shock waves, in the NICFD and in the non-classical regime.

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Fluid-Structure Simulation of a Piston Shock-Tube Using an Adaptive ALE Scheme in the Non-ideal Compressible-Fluid Regime

Guardone

2021

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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Assessment of grid adaptation criteria for steady, two-dimensional, inviscid flows in non-ideal compressible fluids

Cited by 11 publications

References 46 publications

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer–Nunziato model

An adaptive ALE scheme for non-ideal compressible fluid dynamics over dynamic unstructured meshes

Fluid-Structure Simulation of a Piston Shock-Tube Using an Adaptive ALE Scheme in the Non-ideal Compressible-Fluid Regime

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