21,471 research outputs found
A discontinuous Galerkin method for a new class of Green-Naghdi equations on simplicial unstructured meshes
In this paper, we introduce a discontinuous Finite Element formulation on
simplicial unstructured meshes for the study of free surface flows based on the
fully nonlinear and weakly dispersive Green-Naghdi equations. Working with a
new class of asymptotically equivalent equations, which have a simplified
analytical structure, we consider a decoupling strategy: we approximate the
solutions of the classical shallow water equations supplemented with a source
term globally accounting for the non-hydrostatic effects and we show that this
source term can be computed through the resolution of scalar elliptic
second-order sub-problems. The assets of the proposed discrete formulation are:
(i) the handling of arbitrary unstructured simplicial meshes, (ii) an arbitrary
order of approximation in space, (iii) the exact preservation of the motionless
steady states, (iv) the preservation of the water height positivity, (v) a
simple way to enhance any numerical code based on the nonlinear shallow water
equations. The resulting numerical model is validated through several
benchmarks involving nonlinear wave transformations and run-up over complex
topographies
A novel 2.5D spectral approach for studying thin-walled waveguides with fluid-acoustic interaction
This paper presents a novel formulation of two spectral elements to study guided waves in coupled problems involving thin-walled structures and fluid-acoustic enclosures. The aim of the proposed work is the development of a new efficient computational method to study problems where geometry and properties are invariant in one direction, commonly found in the analysis of guided waves. This assumption allows using a two-and-a-half dimensional (2.5D) spectral formulation in the wavenumber-frequency domain. The novelty of the proposed work is the formulation of spectral plate and fluid elements with an arbitrary order in 2.5D. A plate element based on a Reissner-Mindlin/Kirchhoff-Love mixed formulation is proposed to represent the thin-walled structure. This element uses approximation functions to overcome the difficulties to formulate elements with an arbitrary order from functions. The proposed element uses a substitute transverse shear strain field to avoid shear locking effects. Three benchmark problems are studied to check the convergence and the computational effort for different strategies. Accurate results are found with an appropriate combination of element size and order of the approximation functions allowing at least six nodes per wavelength. The effectiveness of the proposed elements is demonstrated studying the wave propagation in a water duct with a flexible side and an acoustic cavity coupled to a Helmholtz resonator.Ministerio de EconomÃa y Competitividad BIA2013-43085-P y BIA2016-75042-C2-1-RCentro Informático CientÃfico de AndalucÃa (CICA
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