Three-dimensional unstructured mesh ocean modelling

Pain, Christopher C.; Piggott, Matthew D.; Goddard, A.J.H.; Fang, F.; Gorman, Gerard J.; Marshall, David P.; Eaton, M.D.; Power, P. Wayne; Oliveira, C.R.E. de

doi:10.1016/j.ocemod.2004.07.005

Cited by 172 publications

(114 citation statements)

References 110 publications

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“…This section describes the governing equations, coupling methods and fracture modelling methods used in the two models: "Fluidity" (an unstructured mesh multiphase fluid model [45]) and "Y2D" (a combined finite-discrete element method based solid model [46]). …”

Section: Description Of Compressible Fluid and Fractured Solid Problemsmentioning

confidence: 99%

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Xiao¹,

Yang²,

Fang

et al. 2017

Journal of Computational Physics

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This work presents the first application of a non-intrusive reduced order method to model solid interacting with compressible fluid flows to simulate crack initiation and propagation. In the high fidelity model, the coupling process is achieved by introducing a source term into the momentum equation, which represents the effects of forces of the solid on the fluid. A combined single and smeared crack model with the MohrCoulomb failure criterion is used to simulate crack initiation and propagation. The non-intrusive reduced order method is then applied to compressible fluid and fractured solid coupled modelling where the computational cost involved in the full high fidelity simulation is high. The non-intrusive reduced order model (NIROM) developed here is constructed through proper orthogonal decomposition (POD) and a radial basis function (RBF) multi-dimensional interpolation method.The performance of the NIROM for solid interacting with compressible fluid flows, in the presence of fracture models, is illustrated by two complex test cases: an immersed wall in a fluid and a blasting test case. The numerical simulation results show that the NIROM is capable of capturing the details of compressible fluids and fractured solids while the CPU time is reduced by several orders of magnitude. In addition, the issue of whether or not to subtract the mean from the snapshots before applying POD is discussed in this paper. It is shown that solutions of the NIROM, without mean subtracted before constructing the POD basis, captured more details than the NIROM with mean subtracted from snapshots.

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Section: Description Of Compressible Fluid and Fractured Solid Problemsmentioning

confidence: 99%

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Xiao¹,

Yang²,

Fang

et al. 2017

Journal of Computational Physics

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“…In this article a finite element Bubnov-Galerkin discretisation of the Navier Stokes equations [13] is employed. In this formulation the velocity components and pressure terms of the solution are represented by the expansions,…”

Section: Governing Equationsmentioning

confidence: 99%

“…The equations are first discretised via a finite element Bubnov Galerkin discretisation of the Fluidity model [13] and the POD model is generated through the method of snapshots. In this approach, solutions of the full model are recorded (as a sequence of snapshots), and from this data appropriate basis functions are formed that optimally represent the problem.…”

Section: Introductionmentioning

confidence: 99%

Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

Xiao

Fang²,

Buchan³

et al. 2014

Journal of Computational Physics

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141

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This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations. The novelty of the method lies in its treatment of the equation's non-linear operator, for which a new method is proposed that provides accurate simulations within an efficient framework. The method itself is a hybrid of two existing approaches that have already been developed to treat non-linear operators within reduced order models. The first of these approaches is one that approximates non-linear operators through quadratic expansions, and this is then blended within a second technique known as the Discrete Empirical Interpolation Method (DEIM). The method proposed applies the quadratic expansion to provide a first approximation of the non-linear operator, and DEIM is then used as a corrector to improve its representation. In addition to the treatment of the non-linear operator the POD model is stabilized using a Petrov-Galerkin method. This adds artificial dissipation to the solution of the reduced order model which is necessary to avoid spurious oscillations and unstable solutions.A demonstration of the capabilities of this new approach is provided by simulating a flow past a cylinder and gyre problems. Comparisons are made with other treatments of non-linear operators, and these show the new method to provide significant improvements in the solution's accuracy.

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“…It can capture small-scale structures and large-scale processes simultaneously by adapting the meshes dynamically in time [13][14][15]. In this work, the Navier-Stokes equations are modified to account for the presence of immersed solids in the fluid domain.…”

Section: Mathematical Formulationmentioning

confidence: 99%

An immersed-shell method for modelling fluid–structure interactions

Viré

Xiang

Pain

2015

Phil. Trans. R. Soc. A.

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The paper presents a novel method for numerically modelling fluid-structure interactions. The method consists of solving the fluid-dynamics equations on an extended domain, where the computational mesh covers both fluid and solid structures. The fluid and solid velocities are relaxed to one another through a penalty force. The latter acts on a thin shell surrounding the solid structures. Additionally, the shell is represented on the extended domain by a non-zero shell-concentration field, which is obtained by conservatively mapping the shell mesh onto the extended mesh. The paper outlines the theory underpinning this novel method, referred to as the immersed-shell approach. It also shows how the coupling between a fluid-and a structural-dynamics solver is achieved. At this stage, results are shown for cases of fundamental interest.

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Three-dimensional unstructured mesh ocean modelling

Cited by 172 publications

References 110 publications

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

A non-intrusive reduced-order model for compressible fluid and fractured solid coupling and its application to blasting

Non-linear model reduction for the Navier–Stokes equations using residual DEIM method

An immersed-shell method for modelling fluid–structure interactions

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