## Lattice Boltzmann Method-1

Kinetic Theory and micro-macro relations Pressure and Temperature are related to kinetic energy of particle as, Phase space and probability distribution function A coordinate system comprising position and velocity can be used to express the dynamics of a system. Such a system is called phase space. In general, the dynamics of a point in the …

## Governing equations

Notes from my favorite books and Material, substantial or total derivative The conservation laws like mass, momentum and energy naturally apply to moving material volumes of fluids, i.e., Lagrangian frame of reference . Hence we need to translate those into Eulerian reference frame, using Reynolds Transport Theorem Reynolds Transport Theorem Where, For the fixed control …

## Multiphase flow modelling – 2: Lagrangian particle tracking

Parameters Maximum number of particles: npmax Particle diameter: dp Particle density: rhop Fluid density: rhof Particles flow rate: PFR (number of particles entering per second) Particle inlet velocity: up_in Two-way coupling(Boolean): use_twoway Define a derived data type for particle with following detail double x, y : position int i,j : mesh location double u,v : …

## Multiphase flow modelling – 1: Development of a basic flow solver

learned from Oliver Desjardins’ lecture (notes) Development of a basic flow solver Incompressible flow Structured 2D staggered grid P-U coupling by Fractional Step Method(simplified version of Kim and Moin, 1985) 2d N-S eqn Spatial discretization Gradient and Laplacian term of pressure by standard second order central differensing scheme. The fractional step method Original fractional step …

## SIMPLE scheme (2/3): Openfoam implementation-SimpleFoam

A walk through SimpleFoam wiki page . This is my study note of simpleFoam wiki page with links that helped me understand. Before simple loop createFields.H The included file createFields.H creates volumeScalarField p and volVectorField U from the 0 directory. Then it includes createPhi.H which creates surfaceScalarField phi with value fvc::flux(U) : It calls the …

## gaussLaplacianScheme(3/3): Adding source terms – fvOptions

Here, we continue the modification of the solver myThermalConductionSolver using fvOptions. Please see the previous post Effect of adding source su =1, sp = 0 case If we keep su=1 in constant/tansportProperties, the source is modified from 9(-150 -80 -80 -70 0 0 -130 -60 -60) to 9(-150.01 -80.01 -80.01 -70.01 -0.01 -0.01 -130.01 -60.01 …

## gaussLaplacianScheme(1/3): Theory and implementation in OpenFOAM

How the discretisation of the laplacian term is done? explicit evaluations, orthogonal corrections … Notes made while reading through report by Jesper Roland. This report has detailed explanation on laplacianScheme abstract class, various macros like TypeName, New,… etc. Options for laplacian scheme A typical system/fvSchemes will read like below: Gauss is the only laplacian scheme …

## c++ : 1 – basics of templates

Understanding of templates is really essential to learn OpenFOAM programming. I moved to learn templates as I stumbled upon gaussLaplacianScheme.C

## Source term linearisation and Under-relaxation

as I learned from the awesome book If properly handled, source term improves solution stability. Consider a discretised conservation equation for a general variable with source in element C written below: If the RHS is large compared to the rest of the terms, the rate of convergence will be affected. In such cases, the rate …

## gaussLaplacianScheme(2/3): A test case in OpenFOAM

as I learned from the awesome book and from several posts in cfdonline This article is an outcome of an effort to learn programming in OpenFOAM. A basic conduction solver is made for the learning purpose. It is decided to document the same for the future reference. Understanding the fvMatrix (“A” matrix of Ax = …