A boundary-domain integral method for the solution of general transport phenomena incompressible fluid motion given by the Navier-Stokes equation set is presented. Velocity-vorticity formulation of the conservations is employed. Different integral representations for conservation field functions based on different fundamental solutions are developed. Special attention is given to the use of subdomain technique and Krylov subspace iterative solvers. The computed solutions of several benchmark problems agree well with available experimental and other computational results.

Computational fluid dynamics by boundary–domain integral method

Very fast development of computing enabled also the development of numerical fluid dynamics. It is numerical modelling and simulation of flow circumstances, including numerical experiments by the computer. Such procedure may have several important advantages over physical measurements on a laboratory model. It is of great importance that fluid properties (density, viscosity, compressibility, etc.) may be simply and arbitrarily changed, numerical experiment does not disturb the flow, plane flows can simply be simulated what may not be the case with laboratory experiments. The numerical experiment also has its own drawbacks and disadvantages, known to all numerical procedures, since the numerical solution represents a result of a discrete equation systems, which are not completely identical to basic physical laws of mechanics of continua. Discretisation often changes quantitatively and qualitatively the behavior of equations and thus also the solutions. Numerical simulation has also similar limitations like a laboratory experiments, since the solutions are individual discrete values only, not the functions of the flow fields.

Computational Fluid Dynamics by the Boundary-Domain Integral Method

A numerical method for the solution of the Navier‐Stokes equations is developed using an integral representation of the conservation equations. The velocity‐vorticity formulation is employed, where the kinematics is given with the Poisson equation for a velocity vector, while the kinetics is represented with the vorticity transport equation. The corresponding boundary‐domain integral equations are presented along with discussions of the kinetics and kinematics of the fluid flow problem. The boundary‐domain integral formulation is developed and tested for natural convection flows in closed cavities with complex geometries.

Natural convection flows in complex cavities by BEM

The paper deals with the numerical solution of fluid dynamics (transport phenomena in incompressible fluid flow) using a boundary-domain integral method. A velocity-vorticity formulation of the Navier-Stokes equations is adopted, where the kinematic equation is written in its parabolic version.

Boundary-domain integral method using a velocity-vorticity formulation

The paper deals with the Boundary Element Method (BEM) for modelling 2D unsteady laminar flow using stream function‐vorticity formulation of the Navier‐Stokes equations. The numerical algorithm for solving a general parabolic diffusion‐convection equation is based on linear mixed elements and a multidomain model also known as subdomain technique. Robustness, accuracy and economy of the developed numerical algorithm is shown on a standard case of steady backward facing step flow and a periodic flow past a circular cylinder test case.

A multidomain boundary element method for unsteady laminar flow using stream function-vorticity equations

The partial differential equations set, governing the laminar motion of viscous incompressible fluid is known as nonlinear Navier-Stokes equation. They constitute the statement of the basic conservation ballance of mass, momentum, and energy, applied to a control volume, i.e. the Eulerian description. This equation system is generally considered to be the fundamental description for all laminar as well as for turbulent flows, although some statistical averaging procedure is needed (e.g. Reynolds equations for turbulence) to simulate numerically the flow at high Re number values due to the enormous computational effort required.

C. A. Brebbia

Papers

Natural and Forced Convection Simulation Using the Velocity-Vorticity Approach

Analysis of laminar flows with separation using BEM

BEM for laminar motion of isochoric viscous fluid