A lattice Boltzmann (LB) method based on the linearized Boltzmann Bhatnagar-Gross-Krook equation for numerical simulation of oscillatory (unsteady) Stokes flow is proposed. Unlike the conventional (nonlinear) LB method that utilizes the time domain exclusively, the proposed method is formulated in the frequency domain to allow for direct access to the complex-valued stress, force, and velocity ...

The immersed boundary (IB) method is a framework for modeling systems in which an elastic structure is immersed in a viscous incompressible fluid. The IB formulation of such problems describes the elasticity of the structure in Lagrangian form and describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form. Interactions between Lagrangian and Eulerian...

Incompressible two dimensional lattice Boltzmann method (LBM) is adopted to simulate flow inside a pipe commonly called Poiseuille flow. Instead of D2Q9 lattice Boltzmann model, we used an incompressible two-dimensional model, D2Q9i to simulate the flow conditions. At the inlet, velocity boundary condition, while at outlet, pressure boundary condition and at the surfaces, no slip boundary condi...

The Poisson-Boltzmann theory has become widely accepted in modeling electrostatic solvation interactions in biomolecular calculations. However the standard practice of atomic point charges in molecular mechanics force fields introduces singularity into the Poisson-Boltzmann equation. The finite-difference/finite-volume discretization approach to the Poisson-Boltzmann equation alleviates the num...

This paper presents a new approach to verify accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one c...

Article history: Received 14 January 2011 Received in revised form 31 May 2011 Accepted 8 July 2011 Available online xxxx