Chapter 19. Adapting the Mesh The solution-adaptive mesh refinement feature of ANSYS FLUENT allows you to refine and/or coarsen your mesh based on geometric and numerical solution data. In addition, ANSYS FLUENT provides tools for creating and viewing adaption fields customized to particular applications. For information about using mesh adaption in ANSYS FLUENT, see Chapter 27: Adapting the Mesh in the separate User’s Guide. Theoretical information about the adaption process is described in detail in the following sections. • Section 19.1: Static Adaption Process • Section 19.2: Boundary Adaption • Section 19.3: Gradient Adaption • Section 19.4: Dynamic Gradient Adaption • Section 19.5: Isovalue Adaption • Section 19.6: Region Adaption • Section 19.7: Volume Adaption • Section 19.8: Yplus/Ystar Adaption • Section 19.9: Anisotropic Adaption • Section 19.10: Geometry-Based Adaption • Section 19.11: Registers Release 12.0 c ANSYS, Inc. January 29, 2009 19-1 Adapting the Mesh 19.1 Static Adaption Process The adaption process is separated into two distinct tasks. 1. The individual cells are marked for refinement or coarsening based on the adaption function, which is created from geometric and/or solution data. 2. The cell is refined or considered for coarsening based on these adaption marks. The primary advantages of this modularized approach are the abilities to create sophisticated adaption functions and to experiment with various adaption functions without modifying the existing mesh. i Write a case and data file before starting the adaption process. If you generate an undesirable mesh, you can restart the process with the saved files. 19.1.1 Hanging Node Adaption Hanging node adaption is the procedure used in ANSYS FLUENT. Meshes produced by this method are characterized by nodes on edges and faces that are not vertices of all the cells sharing those edges or faces, as shown in Figure 19.1.1. Hanging Node Figure 19.1.1: Example of a Hanging Node Hanging node mesh adaption provides the ability to operate on meshes with a variety of cell shapes, including hybrid meshes. Although the hanging node scheme provides significant mesh flexibility, it requires additional memory to maintain the mesh hierarchy which is used by the rendering and mesh adaption operations. 19-2 Release 12.0 c ANSYS, Inc. January 29, 2009 19.1 Static Adaption Process Hanging Node Refinement The cells marked for refinement are divided as described here: • A triangle is split into 4 triangles. • A quadrilateral is split into 4 quadrilaterals. • A tetrahedron is split into eight tetrahedra. The subdivision consists of trimming each corner of the tetrahedron, and subdividing the enclosed octahedron by intro- ducing the shortest diagonal. • A hexahedron is split into 8 hexahedra. • A wedge (prism) is split into 8 wedges. • A pyramid is split into 6 pyramids and 4 tetrahedra. Figures 19.1.2 and 19.1.3 illustrate the division of the supported cell shapes. To maintain accuracy, neighboring cells are not allowed to differ by more than one level of refinement. This prevents the adaption from producing excessive cell volume variations (reducing truncation error) and ensures that the positions of the parent (original) and child (refined) cell centroids are similar (reducing errors in the flux evaluations). Triangle Quadrilateral Figure 19.1.2: Hanging Node Adaption of 2D Cell Types Hanging Node Coarsening The mesh is coarsened by reintroducing inactive parent cells (uniting the child cells to reclaim the previously subdivided parent cell). An inactive parent cell is reactivated if all its children are marked for coarsening. You will eventually reclaim the original mesh with repeated application of the hanging node coarsening. Using the hanging node adaption process, you cannot coarsen the mesh further than the original mesh. Release 12.0 c ANSYS, Inc. January 29, 2009 19-3 Adapting the Mesh Tetrahedron Hexahedron Prism/Wedge Pyramid Figure 19.1.3: Hanging Node Adaption of 3D Cell Types 19-4 Release 12.0 c ANSYS, Inc. January 29, 2009 19.2 Boundary Adaption 19.2 Boundary Adaption If more cells are required on a boundary, they can be added using boundary adaption, which allows you to mark or refine cells in the proximity of the selected boundary zones. The ability to refine the mesh near one or more boundary zones is provided because important fluid interactions often occur in these regions. Example, development of strong velocity gradients in the boundary layer near a wall. An example of a mesh that can be improved with boundary adaption is shown in Fig- ure 19.2.1. This mesh has only two cells on the vertical face of a step. Boundary adaption on the zone corresponding to the face of the step can be used to increase the number of cells, as shown in Figure 19.2.2. This procedure cannot increase the resolution of a curved surface. Therefore, if more cells are required on a curved surface where the shape of the surface is important, create the mesh with sufficient surface nodes before reading it into the solver. 19.3 Gradient Adaption The gradient adaption function allows you to mark cells or adapt the mesh based on the gradient, curvature, or isovalue of the selected field variables. Information can be found in the following subsections: • Section 19.3.1: Gradient Adaption Approach • Section 19.3.2: Example of Steady Gradient Adaption 19.3.1 Gradient Adaption Approach Solution-adaptive mesh refinement is performed to efficiently reduce the numerical er- ror in the digital solution, with minimal numerical cost. Unfortunately, direct error estimation for point-insertion adaption schemes is difficult because of the complexity of accurately estimating and modeling the error in the adapted meshes. A comprehensive mathematically rigorous theory for error estimation and convergence is not yet available for CFD simulations. Assuming that maximum error occurs in high-gradient regions, the readily available physical features of the evolving flow field may be used to drive the mesh adaption process. Release 12.0 c ANSYS, Inc. January 29, 2009 19-5 Adapting the Mesh Grid Figure 19.2.1: Mesh Before Adaption Grid Figure 19.2.2: Mesh after Boundary Adaption 19-6 Release 12.0 c ANSYS, Inc. January 29, 2009 19.3 Gradient Adaption Three approaches for using this information for mesh adaption are available in ANSYS FLUENT: • Gradient approach: In this approach, ANSYS FLUENT multiplies the Euclidean norm of the gradient of the selected solution variable by a characteristic length scale [68]. For example, the gradient function in two dimensions has the following form: r |ei1| = (Acell) 2 |∇f| (19.3-1) where ei1 is the error indicator, Acell is the cell area, r is the gradient volume weight, and ∇f is the Euclidean norm of the gradient of the desired field variable, f. The default value of the gradient volume weight is unity, which corresponds to full volume weighting. A value of zero will eliminate the volume weighting, and values between 0 and 1 will use proportional weighting of the volume. If you specify adaption based on the gradient of a scalar, then the value of |ei1| is displayed when you plot contours of the adaption function. This approach is recommended for problems with strong shocks, e.g., supersonic inviscid flows. • Curvature approach: This is the equidistribution adaption technique formerly used by ANSYS FLUENT, that multiplies the undivided Laplacian of the selected solution variable by a characteristic length scale [368]. For example, the gradient function in two dimensions has the following form: r 2 |ei2| = (Acell) 2 |∇ f| (19.3-2) where ei2 is the error indicator, Acell is the cell area, r is the gradient volume weight, and ∇2f is the undivided Laplacian of the desired field variable (f). The default value of the gradient volume weight is unity, which corresponds to full volume weighting. A value of zero will eliminate the volume weighting, and values between 0 and 1 will use proportional weighting of the volume. This approach is recommended for problems with smooth solutions. Release 12.0 c ANSYS, Inc. January 29, 2009 19-7 Adapting the Mesh • Isovalue approach: This approach is not based on derivatives. Instead, the iso- values of the required field variable f, are used to control the adaption. Therefore, the function is of the form: ei3 = f (19.3-3) where ei3 is the error indicator. This approach is recommended for problems where derivatives are not helpful. For example, if you want to refine the mesh where the reaction is taking place, you can use the isovalues of the reaction rate and mark for refinement at high reaction rates. This approach also allows you to customize the criteria for controlling the adaption using custom field functions, user-defined scalars, etc. The length scale is the square (2D) or cube (3D) root of the cell volume. Introducing the length scale allows resolution of both strong and weak disturbances, increasing the potential for more accurate solutions. However, you can reduce or eliminate the volume weighting by changing the gradient Volume Weight in the Mesh Adaption Controls dialog box (see Section 27.12: Mesh Adaption Controls in the separate User’s Guide for details). Any of the field variables available for contouring can be used in the gradient adaption function. These scalar functions include, both geometric and physical features of the numerical solution. Therefore, in addition to traditional adaption to physical features, such as the velocity, you may choose to adapt to the cell volume field to reduce rapid variations in cell volume. In addition to the Standard (no normalization) approach formerly used by ANSYS FLU- ENT, two options are available for Normalization [107]: • Scale, which scales the values of ei1, ei2, or ei3 by their average value in the domain, i.e.: |e | i (19.3-4) |ei| when using the Scale option, suitable first-cut values for the Coarsen Threshold and the Refine Threshold are 0.3 to 0.5, and 0.7 to 0.9, respectively.