scholarly journals WAVE BREAKING USING A ROLLER APPROACH IN A HYBRID FINITE-VOLUME FINITE-DIFFERENCE BOUSSINESQ-TYPE MODEL

2014 ◽  
Vol 1 (34) ◽  
pp. 13
Author(s):  
Benjamin Tatlock ◽  
Riccardo Briganti ◽  
Rosaria E. Musumeci
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Wave Breaking ◽  
Type Model

An assessment of the roller approach for wave breaking in a hybrid finite-volume finite-difference Boussinesq-type model for the surf-zone

2018 ◽  
Vol 73 ◽  
pp. 160-178 ◽  
Author(s):  
Benjamin Tatlock ◽  
Riccardo Briganti ◽  
Rosaria E. Musumeci ◽  
Maurizio Brocchini
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Wave Breaking ◽  
Surf Zone ◽  
Type Model

scholarly journals SERRE GREEN-NAGHDI MODELLING OF WAVE TRANSFORMATION BREAKING AND RUN-UP USING A HIGH-ORDER FINITE-VOLUME FINITE-DIFFERENCE SCHEME

2011 ◽  
Vol 1 (32) ◽  
pp. 13 ◽  
Author(s):  
Marion Tissier ◽  
Philippe Bonneton ◽  
Fabien Marche ◽  
Florent Chazel ◽  
David Lannes
Keyword(s):  
Energy Dissipation ◽  
Finite Difference ◽  
Finite Volume ◽  
Wave Breaking ◽  
Ad Hoc ◽  
Laboratory Data ◽  
Breaking Waves ◽  
Wave Transformation ◽  
Finite Volume Schemes ◽  
Boussinesq Model

In this paper, a fully nonlinear Boussinesq model is presented and applied to the description of breaking waves and shoreline motions. It is based on Serre Green-Naghdi equations, solved using a time-splitting approach separating hyperbolic and dispersive parts of the equations. The hyperbolic part of the equations is solved using Finite-Volume schemes, whereas dispersive terms are solved using a Finite-Difference method. The idea is to switch locally in space and time to NSWE by skipping the dispersive step when the wave is ready to break, so as the energy dissipation due to wave breaking is predicted by the shock theory. This approach allows wave breaking to be handled naturally, without any ad-hoc parameterization for the energy dissipation. Extensive validations of the method are presented using laboratory data.

scholarly journals A multilevel Monte Carlo finite difference method for random scalar degenerate convection–diffusion equations

2017 ◽  
Vol 14 (03) ◽  
pp. 415-454 ◽  
Author(s):  
Ujjwal Koley ◽  
Nils Henrik Risebro ◽  
Christoph Schwab ◽  
Franziska Weber
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Convergence Rate ◽  
Finite Volume ◽  
Monte Carlo Algorithm ◽  
Diffusion Equations ◽  
Entropy Solutions ◽  
Finite Volume Scheme ◽  
Multilevel Monte Carlo ◽  
Convection Diffusion

This paper proposes a finite difference multilevel Monte Carlo algorithm for degenerate parabolic convection–diffusion equations where the convective and diffusive fluxes are allowed to be random. We establish a notion of stochastic entropy solutions to these equations. Our chief goal is to efficiently compute approximations to statistical moments of these stochastic entropy solutions. To this end, we design a multilevel Monte Carlo method based on a finite volume scheme for each sample. We present a novel convergence rate analysis of the combined multilevel Monte Carlo finite volume method, allowing in particular for low [Formula: see text]-integrability of the random solution with [Formula: see text], and low deterministic convergence rates (here, the theoretical rate is [Formula: see text]). We analyze the design and error versus work of the multilevel estimators. We obtain that the maximal rate (based on optimizing possibly the pessimistic upper bounds on the discretization error) is obtained for [Formula: see text], for finite volume convergence rate of [Formula: see text]. We conclude with numerical experiments.

Tracing Streamlines on Unstructured Grids From Finite Volume Discretizations

SPE Journal ◽  
2008 ◽  
Vol 13 (04) ◽  
pp. 423-431 ◽  
Author(s):  
Sebastien F. Matringe ◽  
Ruben Juanes ◽  
Hamdi A. Tchelepi
Keyword(s):  
Finite Element ◽  
Velocity Field ◽  
Finite Difference ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Control Volume ◽  
Next Generation ◽  
Flux Approximation ◽  
Streamline Tracing ◽  
Tracing Method

Summary The accuracy of streamline reservoir simulations depends strongly on the quality of the velocity field and the accuracy of the streamline tracing method. For problems described on complex grids (e.g., corner-point geometry or fully unstructured grids) with full-tensor permeabilities, advanced discretization methods, such as the family of multipoint flux approximation (MPFA) schemes, are necessary to obtain an accurate representation of the fluxes across control volume faces. These fluxes are then interpolated to define the velocity field within each control volume, which is then used to trace the streamlines. Existing methods for the interpolation of the velocity field and integration of the streamlines do not preserve the accuracy of the fluxes computed by MPFA discretizations. Here we propose a method for the reconstruction of the velocity field with high-order accuracy from the fluxes provided by MPFA discretization schemes. This reconstruction relies on a correspondence between the MPFA fluxes and the degrees of freedom of a mixed finite-element method (MFEM) based on the first-order Brezzi-Douglas-Marini space. This link between the finite-volume and finite-element methods allows the use of flux reconstruction and streamline tracing techniques developed previously by the authors for mixed finite elements. After a detailed description of our streamline tracing method, we study its accuracy and efficiency using challenging test cases. Introduction The next-generation reservoir simulators will be unstructured. Several research groups throughout the industry are now developing a new breed of reservoir simulators to replace the current industry standards. One of the main advances offered by these next generation simulators is their ability to support unstructured or, at least, strongly distorted grids populated with full-tensor permeabilities. The constant evolution of reservoir modeling techniques provides an increasingly realistic description of the geological features of petroleum reservoirs. To discretize the complex geometries of geocellular models, unstructured grids seem to be a natural choice. Their inherent flexibility permits the precise description of faults, flow barriers, trapping structures, etc. Obtaining a similar accuracy with more traditional structured grids, if at all possible, would require an overwhelming number of gridblocks. However, the added flexibility of unstructured grids comes with a cost. To accurately resolve the full-tensor permeabilities or the grid distortion, a two-point flux approximation (TPFA) approach, such as that of classical finite difference (FD) methods is not sufficient. The size of the discretization stencil needs to be increased to include more pressure points in the computation of the fluxes through control volume edges. To this end, multipoint flux approximation (MPFA) methods have been developed and applied quite successfully (Aavatsmark et al. 1996; Verma and Aziz 1997; Edwards and Rogers 1998; Aavatsmark et al. 1998b; Aavatsmark et al. 1998c; Aavatsmark et al. 1998a; Edwards 2002; Lee et al. 2002a; Lee et al. 2002b). In this paper, we interpret finite volume discretizations as MFEM for which streamline tracing methods have already been developed (Matringe et al. 2006; Matringe et al. 2007b; Juanes and Matringe In Press). This approach provides a natural way of reconstructing velocity fields from TPFA or MPFA fluxes. For finite difference or TPFA discretizations, the proposed interpretation provides mathematical justification for Pollock's method (Pollock 1988) and some of its extensions to distorted grids (Cordes and Kinzelbach 1992; Prévost et al. 2002; Hægland et al. 2007; Jimenez et al. 2007). For MPFA, our approach provides a high-order streamline tracing algorithm that takes full advantage of the flux information from the MPFA discretization.

scholarly journals Numerical Simulation of Wave Propagation, Breaking, and Setup on Steep Fringing Reefs

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1147 ◽  
Author(s):  
Shanju Zhang ◽  
Liangsheng Zhu ◽  
Jianhua Li
Keyword(s):  
Finite Difference ◽  
Finite Volume ◽  
Boussinesq Equations ◽  
Transformation Process ◽  
Wave Transformation ◽  
Computational Accuracy ◽  
Irregular Wave ◽  
Eddy Viscosity Model ◽  
Fringing Reefs ◽  
Volume Method

The prediction of wave transformation and associated hydrodynamics is essential in the design and construction of reef top structures on fringing reefs. To simulate the transformation process with better accuracy and time efficiency, a shock-capturing numerical model based on the extended Boussinesq equations suitable for rapidly varying topography with respect to wave transformation, breaking and runup, is established. A hybrid finite volume–finite difference scheme is used to discretize conservation form of the extended Boussinesq equations. The finite-volume method with a HLL Riemann solver is applied to the flux terms, while finite-difference discretization is applied to the remaining terms. The fourth-order MUSCL (Monotone Upstream-centered Schemes for Conservation Laws) scheme is employed to create interface variables, with in which the van-Leer limiter is adopted to improve computational accuracy on complex topography. Taking advantage of van-Leer limiter, a nested model is used to take account of both computational run time and accuracy. A modified eddy viscosity model is applied to better accommodate wave breaking on steep reef slopes. The established model is validated with laboratory measurements of regular and irregular wave transformation and breaking on steep fringing reefs. Results show the model can provide satisfactory predictions of wave height, mean water level and the generation of higher harmonics.

scholarly journals Pixels and their neighbors: Finite volume

2016 ◽  
Vol 35 (8) ◽  
pp. 703-706 ◽  
Author(s):  
Rowan Cockett ◽  
Lindsey J. Heagy ◽  
Douglas W. Oldenburg
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Direct Current ◽  
Numerical Results ◽  
Dc Resistivity ◽  
Matrix Representations ◽  
Volume Method

We take you on the journey from continuous equations to their discrete matrix representations using the finite-volume method for the direct current (DC) resistivity problem. These techniques are widely applicable across geophysical simulation types and have their parallels in finite element and finite difference. We show derivations visually, as you would on a whiteboard, and have provided an accompanying notebook at http://github.com/seg to explore the numerical results using SimPEG ( Cockett et al., 2015 ).

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