A general vertical decomposition of Euler equations: Multilayer-moment models

Garres-Díaz, José; Escalante, Cipriano; Luna, Tomás Morales de; Diaz, Manuela

doi:10.1016/j.apnum.2022.09.004

Cited by 6 publications

(4 citation statements)

References 51 publications

(94 reference statements)

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“…Applications of shallow flows can be found in many scientific fields, e.g., in hydrodynamics [31] or granular flows [16]. An important class of problems considers changing topographies, for example related to snow avalanches [15] or sediment transport [17]. The main assumption for the widely used Shallow Water Equations (SWE) is that the horizontal velocity profile is constant along the vertical axis from the bottom to the surface.…”

Section: Introductionmentioning

confidence: 99%

Steady states and well-balanced schemes for shallow water moment equations with topography

Koellermeier

Pimentel-García

2022

Applied Mathematics and Computation

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Section: Introductionmentioning

confidence: 99%

Steady states and well-balanced schemes for shallow water moment equations with topography

Koellermeier

Pimentel-García

2022

Applied Mathematics and Computation

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“…Theorem 4. Let us consider the LIN-H-STRESS model defined by (43) and definitions (41), (44), with the stress tensor components defined by ( 22), ( 24), (26), and the terms 𝐾 𝛼±1/2 , 𝐾 𝑤,𝛼±1/2 given by (18). The following energy balance is satisfied…”

Section: Systems With Viscous Dependent Pressure: Lin-h-stressmentioning

confidence: 99%

“…On the other hand, layer-averaged (or multilayer) models (see [2,21]), which are explained in the following paragraph, have been developed more widely for shallow flows, including its application to non-Newtonian fluids. Interestingly, both approaches can be written in a common framework, as shown in [26]. In that work, authors also proposed the combination of these methods to obtain multilayer-moment models, which are expected to be high-order accurate in the vertical direction, although it has been developed just in the hydrostatic framework for now.…”

Section: Introductionmentioning

confidence: 99%

Layer-averaged approximation of Navier–Stokes system with complex rheologies

Fernández-Nieto

Garres-Díaz

2023

ESAIM: M2AN

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In this work, we present a family of layer-averaged models for the Navier-Stokes equations. For its derivation, we consider a layerwise linear vertical profile for the horizontal velocity component. As a particular case, we also obtain layer-averaged models with the common layerwise constant approximation of the horizontal velocity. The approximation of the derivatives of the velocity components is set by following the theory of distributions to account for the discontinuities at the internal interfaces. Several models has been proposed, depending on the order of approximation of an asymptotic analysis respect to the shallowness parameter. Then, we obtain a hydrostatic model with vertical viscous effects, a hydrostatic model where the pressure depends on the stress tensor, and fully non-hydrostatic models, with a complex rheology. It is remarkable that the proposed models generalize plenty of previous models in the literature. Furthermore, all of them satisfy an exact dissipative energy balance. We also propose a model that is second-order accurate in the vertical direction thanks to a correction of the shear stress approximation. Finally, we show how effective the layerwise linear approach is to notably improve, with respect to the layerwise constant method, the approximation of the velocity profile for some geophysical flows. Namely, a Newtonian fluid and some complex viscoplastic (dry granular and Herschel-Bulkley) materials are considered.

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“…The new system of equations proved to be more accurate than the SWE in numerical simulations [14]. The model was recently extended to the non-hydrostatic case in [17] and generalized to include multi-layer models similar to [4] and [5].…”

Section: Introductionmentioning

confidence: 99%

Projective Integration for Hyperbolic Shallow Water Moment Equations

Amrita

Koellermeier

2022

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In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more complex PDE system. The resulting equations can become stiff depending on the friction parameters, which leads to severe time step constraints of standard numerical schemes. In this paper, we apply Projective Integration schemes to stiff Shallow Water Moment Equations to overcome the time step constraints in the stiff regime and accelerate the numerical computations while still achieving high accuracy. In different dam break and smooth wave test cases, we obtain a speedup of up to 55 with respect to standard schemes.

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A general vertical decomposition of Euler equations: Multilayer-moment models

Cited by 6 publications

References 51 publications

Steady states and well-balanced schemes for shallow water moment equations with topography

Steady states and well-balanced schemes for shallow water moment equations with topography

Layer-averaged approximation of Navier–Stokes system with complex rheologies

Projective Integration for Hyperbolic Shallow Water Moment Equations

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