http://hdl.handle.net/2173/31422 Wed, 22 May 2013 16:24:02 GMT 2013-05-22T16:24:02Z http://hdl.handle.net/2173/108954 Title: Finite volume simulation of viscous free surface waves using the Cartesian cut cell approach Authors: Bai, W.; Mingham, Clive G.; Causon, Derek M.; Qian, Ling Abstract: The application of the Cartesian cut cell approach in the numerical simulation of two-dimensional viscous free surface flows is described. The Arbitrary Lagrangian-Eulerian method is adopted to update the moving free water surface in a semi-Lagrangian scheme, in which a finite volume method of second-order accuracy in space is used for solving the flow field based on an Eulerian description at each time step. The cut cell approach is employed to track the free surface and solid boundaries across a stationary background Cartesian grid covering the whole fluid, air and solid regions. In this approach, the cells full of air and solid are not calculated explicitly, and apart from the fluid cells, cut cells and merged cells are treated separately in terms of corresponding boundary conditions. In order to validate the present numerical method, current flow past a circular cylinder at various low Reynolds numbers and wave sloshing in a rectangular container are tested first. Further numerical results are obtained for the propagation of regular waves and a wave passing over a submerged dike. The model is also applied to the simulation of radiation waves induced by a forced oscillating submerged circular cylinder. The results indicate that the present numerical model using the Cartesian cut cell approach is highly efficient for solving the wave fields, and fully automatic for generating boundary fitted meshes. These features are particularly useful for moving boundary problems in a larger computational domain and with a longer simulation time. Description: Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in International Journal for Numerical Methods in Fluids, published by and copyright John Wiley & Sons Ltd.. Thu, 01 Jan 2009 00:00:00 GMT http://hdl.handle.net/2173/108954 2009-01-01T00:00:00Z http://hdl.handle.net/2173/35234 Title: Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations Authors: Hu, Keming; Mingham, Clive G.; Causon, Derek M. Abstract: A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool. Description: Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in Coastal engineering, published by and copyright Elsevier. Wed, 01 Nov 2000 00:00:00 GMT http://hdl.handle.net/2173/35234 2000-11-01T00:00:00Z http://hdl.handle.net/2173/35234 Title: Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations Authors: Hu, Keming; Mingham, Clive G.; Causon, Derek M. Abstract: A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool. Description: Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in Coastal engineering, published by and copyright Elsevier. Wed, 01 Nov 2000 00:00:00 GMT http://hdl.handle.net/2173/35234 2000-11-01T00:00:00Z http://hdl.handle.net/2173/35232 Title: A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations Authors: Shiach, Jon B.; Mingham, Clive G. Abstract: A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments. Description: Full-text of this article is not available in this e-prints service. This article was originally published following peer-review in Coastal engineering, published by and copyright Elsevier. Tue, 01 Jan 2008 00:00:00 GMT http://hdl.handle.net/2173/35232 2008-01-01T00:00:00Z