An Ocean Circulation Model Based on Operator-Splitting, Hamiltonian Brackets, and the Inclusion of Sound Waves

2009 ◽  
Vol 39 (7) ◽  
pp. 1615-1633 ◽  
Author(s):  
Rick Salmon
Keyword(s):  
Lattice Boltzmann Method ◽  
Ocean Circulation ◽  
Lattice Boltzmann ◽  
Circulation Model ◽  
Sound Waves ◽  
Ocean Circulation Model ◽  
Time Step ◽  
Model Based ◽  
Strang Splitting ◽  
Boltzmann Method

Abstract This paper offers a simple, entirely prognostic, ocean circulation model based on the separation of the complete dynamics, including sound waves, into elementary Poisson brackets. For example, one bracket corresponds to the propagation of sound waves in a single direction. Other brackets correspond to the rotation of the velocity vector by individual components of the vorticity and to the action of buoyancy force. The dynamics is solved by Strang splitting of the brackets. Key features of the method are the assumption that the sound waves propagate exactly one grid distance in a time step and the use of Riemann invariants to solve the sound-wave dynamics exactly. In these features the method resembles the lattice Boltzmann method, but the flexibility of more conventional methods is retained. As in the lattice Boltzmann method, very short time steps are required to prevent unrealistically strong coupling between the sound waves and the slow hydrodynamic motions of primary interest. However, the disadvantage of small time steps is more than compensated by the model’s extreme simplicity, even in the presence of very complicated boundaries, and by its massively parallel form. Numerical tests and examples illustrate the practicality of the method.

A Meshfree-Based Lattice Boltzmann Approach for Simulation of Fluid Flows Within Complex Geometries

2018 ◽  
pp. 188-222 ◽  
Author(s):  
Sonam Tanwar
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Moving Boundary ◽  
Fluid Flows ◽  
Computational Domain ◽  
Time Step ◽  
Boundary Problems ◽  
Complex Process ◽  
Element Free ◽  
Boltzmann Method

This chapter develops a meshless formulation of lattice Boltzmann method for simulation of fluid flows within complex and irregular geometries. The meshless feature of proposed technique will improve the accuracy of standard lattice Boltzmann method within complicated fluid domains. Discretization of such domains itself may introduce significant numerical errors into the solution. Specifically, in phase transition or moving boundary problems, discretization of the domain is a time-consuming and complex process. In these problems, at each time step, the computational domain may change its shape and need to be re-meshed accordingly for the purpose of accuracy and stability of the solution. The author proposes to combine lattice Boltzmann method with a Galerkin meshfree technique popularly known as element-free Galerkin method in this chapter to remove the difficulties associated with traditional grid-based methods.

scholarly journals Development of hybrid model based on Lattice Boltzmann Method and Cellular Automata devoted for phase transformation – simulation of heat flow with consideration of enthalpy

2018 ◽  
Vol 240 ◽  
pp. 01020
Author(s):  
Łukasz Łach ◽  
Robert Straka ◽  
Dmytro Svyetlichnyy
Keyword(s):  
Heat Transfer ◽  
Phase Transformation ◽  
Heat Flow ◽  
Lattice Boltzmann Method ◽  
Hybrid Model ◽  
Lattice Boltzmann ◽  
Model Based ◽  
Diffusion Phase ◽  
Boltzmann Method ◽  
New Phase

In heat treatment of materials, the phase transformation is an important phenomenon, which determines the final microstructure. The microstructure of different materials described by such parameters as morphology, grain size, phase fraction and their spatial distribution, largely effects on the mechanical and functional properties of final products. The subject of the work is a development of a hybrid model based on CA and Lattice Boltzmann method (LBM) for modeling of the diffusion phase transformation. The model has a modular structure and simulates three basic phenomena: diffusion, heat flow and phase transformation. The objective of the paper is a presentation of module of the hybrid model for simulation of heat flow with considering of enthalpy of transformation. This is one of the stages in the development of the model and obtained results will be used in a combined solution of heat transfer and diffusion during the modeling of diffusion phase transformations. Lately, the model will be extended to three dimensions and will use hybrid computational systems (CPU and GPU). CA and LBM are used in the model as follows. LBM is used for modeling of heat flow, while CA is used for modeling of microstructure evolution during the phase transformation. The main factors considered in the model are the enthalpy of transformation and heat transfer. The paper presents the results of the modeling of the new phase growth determined by different values of overcooling affecting on different values in the enthalpy of transformation. The heat flow is simulated and the results for some modeling variants are shown. Examples of simulation results obtained from the modeling are presented in the form of images, which present the growth of new phase and temperature distributions.

An Improved Lattice Boltzmann Method for Steady Fluid Flows

2004 ◽  
Author(s):  
Aditya C. Velivelli ◽  
Kenneth M. Bryden
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Finite Difference Methods ◽  
Nonlinear Partial Differential Equation ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Flow Problems ◽  
Computational Performance ◽  
Boltzmann Method

The use of the lattice Boltzmann method in computational fluid dynamics has been steadily increasing. The highly local nature of lattice Boltzmann computations have allowed for easy cache optimization and parallelization. This bestows the lattice Boltzmann method with considerable superiority in computational performance over traditional finite difference methods for solving unsteady flow problems. When solving steady flow problems, the explicit nature of the lattice Boltzmann discretization limits the time step size. The time step size is limited by the Courant-Friedrichs-Lewy (CFL) condition and local gradients in the solution, the latter limitation being more extreme. This paper describes a novel explicit discretization for the lattice Boltzmann method that can perform simulations with larger time step sizes. The new algorithm is applid to the steady Burger’s equation, uux = μ(uxx + uyy), which is a nonlinear partial differential equation containing both convection and diffusion terms. A comparison between the original lattice Boltzmann method and the new algorithm is performed with regard to time for computation and accuracy.

Sign in / Sign up

Export Citation Format

Share Document