Nomenclature
Chapter 2 2.0 LITERATURE REVIEW
3.4 Predefined Parameters
3.5.2 CFD Grid /Mesh Generation and Discretization Methods
In order to generate the highest quality of grids for the highest level of accuracy on a CFD simulation, grids generated depends on the complexity of the flow problem. For high complex flow problems, a more complex high quality grids need to be generated for the CFD simulation. This high level of flow complexity applies for automotive type problems. 1-lowever, the applications of complex grid generation in automotive flow problems are dependent on the overall performance of the modern day computers. The generation of grids and employing of discretization schemes for a simplified flow were done using a linear or potential flow method.
After the development of supercomputers that are capable in handling complex turbulence flows, a non-linear method was developed for grid generation and discretization schemes.
The linear methods or potential flow methods are applied on problems where flow is usually incompressible, inviscid and irrotational. Governing Navier-Stokes equation is
reduced to its linear Laplace form. Flow that uses the linear methods are not practical in solving turbulent flow around a ground vehicle. This is because grid generation for a linear method is usually generated only on the body surface of the ground vehicle geometry. Despite its limitations, the linear methods are still widely used in the industry.
However, modeling additional flow phenomena such as vehicle wake and vortex thrmation requires separate modeling techniques. it does not have the ability to automatically simulate flow separations around the vehicle especially the formation of A- pillar vortices. Further information on the linear methods is available in Ahmed (1998).
In the non-linear methods, the physics of the flow takes into account of complex phenomenon such as turbulent properties. Therefore, it requires a much more complex Navier-stokes equation. Since three-dimensionality is now in play, grids generation will occupy the whole computational domain around the geometry of the ground vehicle body.
For non-linear methods, the coupling of grid generations and discretization of numerical schemes approximations can be done using either one of three grids discretization methods:
• Finite Difference
e Finite Volume
• Finite Element
The choice of using the finite difference, finite volume or finite element methods depends on the complexity of the geometry.
According to Ahmed (1998), the finite difference technique was the first to he developed.
The basic idea of finite difference technique is to express the governing partial differential equations approximately into algebraic difference equations form using finite difference schemes at the grid nodal point. Finite difference methods often employ curvilinear orthogonal grid system that are difficult and time consuming to generate especially in three-dimensional computational domain. The resulting governing transport equations have more terms. This difficulty makes the finite difference techniques seldom used in automotive CFD.
In the finite volume methods, the computational domain is split up into many small control volumes. The partial differential governing equations are integrated over each of 63
the control volumes and the resulting integrated governing equations are then discretized using finite-difference schemes. A resulting set of algebraic equations is then formed, which are then solved. The main advantage of finite volume methods over the finite difference methods is that the finite volume methods can use both structured orthogonal and non-orthogonal grid system. In the non-orthogonal grid system, irregular unstructured grids can be used. As a result, various grid shapes and size can be used for the finite volume methods. This is however, at the expense of additional computational resource, Because of the flexibility in grid generation of the finite volume methods, it is the most preferable methods used in automobile aerodynamics applications.
In the finite element methods, the computational domain is split up into small volumes, called elements. Within each element, values are being approximated as a liner combination of weighting residuals and use the integral form of the governing differential equations for each element volume without direct reference to other cells. Infonnation is shared among all the other grid points in the element. This method generally uses irregular unstructured grid, often in a triangular shaped element. By employing irregular unstructured grids, the treatment of complex surface geometry is possible and furthermore, it also allows local grid refinements at critical areas without the penalty of simultaneous grid refinements at other areas. However, this also serves as a disadvantage since sufficient refined grids in finite element methods are needed to give solution of high accuracy, Du Pont (2001).
For structured grids, the computational domain is often divided into several blocks. This technique is often defined as Block-Structured or Multi-Block technique. Each block can be constructed with different grid density depending on the flow requirement on that region (i. e. separation, vortex generation). Often in a three-dimensional flow, hexahedral type grid is used for the computational domain. Ilexahedral grids have small no skewness resulting in numerical results of high accuracy. The problem with multi-block structured grid is that most often, the grids do not align up against its adjacent interface of blocks.
Grids can also be arranged in an unstructured manner. in three-dimensional flow, grids that are normally arranged in an unstructured manner consist of prisms and tetrahedral grids. Unstructured grids offer flexibility and in especially on area with complex surface geometry. The overall grid generation process is faster with unstructured grids.
Figure 3.5. 1 (a, b, C): Grids in different aspect ratio.
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The present work was conducted by using a ANSYS- 11 Software to generated the grid.
The unstructured grid used contained about maximum 2096000 elements and 467000 nodes. We considered 12 grid layers in the boundary layer of the body.
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