The default convergence criterion for all residuals is set to a value of 1x10-3, except the energy* residual, for which the default criterion is 1x10-6. The solver iterates until it reaches the convergence criteria. Table 1 shows the number of iterations required for each residual and the variation of residuals with different convergence criterion. It can be observed that the smaller the convergence criterion value is, the smaller the residual values are. Hence, smaller residual values will produce more accurate results but the solver will take more iteration to converge (more power and time is used). Convergence Criterion Iterations Continuity Energy* 1.00E-02 1.00E-03 1.00E-04 1.00E-02 1.00E-03 1.00E-04 38 46 55 55 70 84 Quadrilateral Mesh 3.43E-04 9.31E-07 6.02E-05 1.35E-07 7.13E-06 1.22E-08 Triangular Mesh 9.92E-04 4.22E-07 8.97E-05 2.95E-08 9.03E-06 2.24E-09 k Epsilon
3.37E-04 2.81E-04 8.54E-05 7.22E-05 6.40E-06 5.38E-06 1.06E-04 1.55E-04 1.09E-05 1.63E-05 1.16E-06 1.74E-06
Table 1 Residual Values Obatined from Different Convergence Criterion
Additionally, at the same value of convergence criterion, the number of iteration for triangular mesh is more than that of quadrilateral mesh. As a result, the triangular mesh contains more cells and finer cells.
Figure 1a Temperature Contour (10^3)
Figure 1b Temperature Contour (10^5)
Figure 1a and Figure 1b shows the temperature contour using the same triangular mesh but with different convergence criteria. There is no evident difference between these two graphs, meaning it is not necessary to further reduce the convergence criteria in this case. The convergence criteria of 10-3 is sufficiently accurate in this case. Therefore, the following results and discussions are taken using convergence criteria of 10-3.
2.0 Effect of Alternating the Order of Discretization and Mesh Adaption The Navier-Stokes equation needs to be solved to obtain the flow features. In almost every real situation, the NavierStokes equations are a set of nonlinear partial differential equations which describe the motion of fluid flow. Thus, it is impossible to solve these equations numerically. FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations that can be solved numerically. This control volume technique consists of integrating the governing equations about each control volume, yielding discrete equations that conserve each quantity on a control-volume basis.
Shu Yue (Amy) Xiao 7385167 Modelling&Simulation III
When first-order accuracy is desired, quantities at cell faces are determined by assuming that the cell-centre values of any field variable represent a cell-average value and hold throughout the entire cell; the face quantities are identical to the cell quantities. Thus when first-order scheme is selected, the face value is set equal to the cell-centre value of the cell. When second-order accuracy is desired, quantities at cell faces are computed using a multidimensional linear reconstruction approach. In this approach, higher-order accuracy is achieved at cell faces through a Taylor series expansion of the cell-cantered solution about the cell centroid.
Figure 2a Temperature contour for 1st order solution
Figure 2bTemperature contour for 2nd order solution
Figure 2a is the temperature contour obtained using first order discretisation in triangular mesh. It can be found that the temperature inlets satisfy the boundary conditions but the pressure outlet is very diffusive, and mixing is over predicted. According to Figure 2b (using second order discretisation), the general temperature contour is similar to that obtained using first order discretisation. However, the solutions are less diffusive. This is because numerical discretisation errors generated using the second order approximation are less than those...