# The Scaled Equation Of State

1476 WordsMar 16, 20166 Pages
The scaled equation of state is (2.66) Coordinate transformation In rare case may be done a numerical solution in a Cartesian coordinate system. For numerical simulations is used usually a curve coordinate system. In order to prevent of geometric errors in solutions in finite volume methods, is necessary to the precise determinationof Surface vector.As an example of an airfoilwhich can be describedwith difficulty the curve of airfoil by Cartesian grid point and points lie within the airfoil. Figure 1.2) grid system Therefore it is better to select a curve coordinate system. As is shown in figure1-2. Due to this coordinate transformation increase indeed complexity of equation with respect to Cartesian form but has many advantageous like improvement of efficient and accuracy in numerical method. In the transformation from the physical domain to the computational domain, a one to onetransformation is assumed.That is, a point in thephysical domain, say point A, corresponds to oneand only one point in the computational domain, point B, and vice versa. Figure 2.2) Grid configuration in physical domain (left) and computational domain (right) Due to the transformation the transition from a curvilinear non-orthogonal physical domain is carried out on an orthogonal computational domain (Figure2-2). Almost infinitely complex body boundaries in physical space are converted to rectangular plane in the computational space. Metrics of Transformation The physical domain and the