Borja Servan-Camas

Non-negativity and stability analyses of lattice Boltzmann method for advection-diffusion equation

Stability is one of the main concerns in the lattice Boltzmann method (LBM). The objectives of this study are to investigate the linear stability of the lattice Boltzmann equation with the Bhatnagar-Gross-Krook collision operator (LBGK) for the advection-diffusion equation (ADE), and to understand the relationship between the stability of the LBGK and non-negativity of the equilibrium distribution functions (EDFs). This study conducted linear stability analysis on the LBGK, whose stability depends on the lattice Peclet number, the Courant number, the single relaxation time, and the flow direction. The von Neumann analysis was applied to delineate the stability domains by systematically varying these parameters. Moreover, the dimensionless EDFs were analyzed to identify the non-negative domains of the dimensionless EDFs. As a result, this study obtained linear stability and non-negativity domains for three different lattices with linear and second-order EDFs. It was found that the second-order EDFs have larger stability and non-negativity domains than the linear EDFs and outperform linear EDFs in terms of stability and numerical dispersion. Furthermore, the non-negativity of the EDFs is a sufficient condition for linear stability and becomes a necessary condition when the relaxation time is very close to 0.5. The stability and non-negativity domains provide useful information to guide the selection of dimensionless parameters to obtain stable LBM solutions. We use mass transport problems to demonstrate the consistency between the theoretical findings and LBM solutions.

Accelerated 3D multi-body seakeeping simulations using unstructured finite elements

Being capable of predicting seakeeping capabilities in the time domain is of great interest for the marine and offshore industries. However, most computer programs used work in the frequency domain, with the subsequent limitation in the accuracy of their model predictions. The main objective of this work is the development of a time domain solver based on the finite element method capable of solving multi-body seakeeping problems on unstructured meshes. In order to achieve this objective, several techniques are combined: the use of an efficient algorithm for the free surface boundary conditions, the use of deflated conjugate gradients, and the use of a graphic processing unit for speeding up the linear solver. The results obtained by the developed model showed good agreement with analytical solutions, experimental data for an actual offshore structure model, as well as numerical solutions obtained by other numerical method. Also, a simulation with sixteen floating bodies was carried out in an affordable CPU time, showing the potential of this approach for multi-body simulation.

A non-linear finite element method on unstructured meshes for added resistance in waves

ABSTRACT In this work a finite element method is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration; and the second one based on the streamline-upwind Petrov–Galerkin stabilisation. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.In this work a finite element method is proposed to solve the problem of estimating the added resistance of a ship in waves in the time domain and using unstructured meshes. Two different schemes are used to integrate the corresponding free surface kinematic and dynamic boundary conditions: the first one based on streamlines integration; and the second one based on the streamline-upwind Petrov–Galerkin stabilisation. The proposed numerical schemes have been validated in different test cases, including towing tank tests with monochromatic waves. The results obtained in this work show the suitability of the present method to estimate added resistance in waves in a computationally affordable manner.

Advances in the Development of a Time-Domain Unstructured Finite Element Method for the Analysis of Waves and Floating Structures Interaction

Being capable of predicting wave-structure interaction in the time domain is of great interest for the offshore industry. However, most computer programs used in the industry work in the frequency domain. Therefore, the main objective of this work is the development a time domain solver based on the finite element method capable of solving wave-structure interaction problems using unstructured meshes. We found good agreement between the numerical results we obtained and analytical solutions as well as numerical solutions obtained by other numerical method.

Lattice Boltzmann Method in Saltwater Intrusion Modeling

This study develops a saltwater intrusion simulation model using a lattice Boltzmann method (LBM) in a two-dimensional coastal confined aquifer. The saltwater intrusion phenomenon is described by density-varied groundwater flow and mass transport equations, where a freshwater-saltwater mixing zone is considered. Although primarily developed using the mesoscopic approach to solve macroscopic fluid dynamic problems, e.g., Navier-Stoke equation, LBM is able to be adopted to solve physical-based diffusion-type governing equations as for the groundwater flow and mass transport equations. In this study, the density-varied groundwater flow equation and the advection-dispersion equation (ADE) are modeled by the lattice Boltzmann method. Under the consideration on the steadystate groundwater flow due to low storativity, in each time step the flow problem is modified to be a Poisson equation and solved by LBM. Nevertheless, the groundwater flow is still a time-marching problem with spatial-temporal variation in salinity concentration as well as density. The Henry problem is used to compare the LBM results against the Henry solution.