A platform for research: civil engineering, architecture and urbanism
A platform for research: civil engineering, architecture and urbanism
From the Lattice Boltzmann Equation to Fluid Governing Equations
In this chapter, we derive the fluid governing equationsFluid governing equation (the continuityFluid governing equationmass conservation and Navier‒StokesFluid governing equationNavier-Stokes equation (NSE) equations) from the lattice Boltzmann equation (LBE)Fluid governing equationlattice Boltzmann equation (LBE). By the end of this chapter, readers will realize that the LBE is equivalent to the fluid governing equations. To a certain extent, the fluid governing equations are a 2nd-order approximate solution to the LBE. We do not cover the energy equation derivation in this chapter because this book mainly deals with isothermal built environment problems. The purpose of this chapter is to deepen the reader’s understanding of the LBM. The derivation process involves several mathematical tools, including partial differentiation, integration, and simple linear algebra. Readers not interested in such mathematical details can skip this chapter if they wish, which will not affect their general understanding and knowledge needed to apply the LBM to solve engineering problems.
From the Lattice Boltzmann Equation to Fluid Governing Equations
In this chapter, we derive the fluid governing equationsFluid governing equation (the continuityFluid governing equationmass conservation and Navier‒StokesFluid governing equationNavier-Stokes equation (NSE) equations) from the lattice Boltzmann equation (LBE)Fluid governing equationlattice Boltzmann equation (LBE). By the end of this chapter, readers will realize that the LBE is equivalent to the fluid governing equations. To a certain extent, the fluid governing equations are a 2nd-order approximate solution to the LBE. We do not cover the energy equation derivation in this chapter because this book mainly deals with isothermal built environment problems. The purpose of this chapter is to deepen the reader’s understanding of the LBM. The derivation process involves several mathematical tools, including partial differentiation, integration, and simple linear algebra. Readers not interested in such mathematical details can skip this chapter if they wish, which will not affect their general understanding and knowledge needed to apply the LBM to solve engineering problems.
From the Lattice Boltzmann Equation to Fluid Governing Equations
Han, Mengtao (author) / Ooka, Ryozo (author)
2023-05-30
19 pages
Article/Chapter (Book)
Electronic Resource
English