1. Mesh uncurving

As high order numerical methods require a high order representation of the boundary, a number of methods have been developed to provide this level of accuracy. In some curving techniques, such as agglomerated meshes, it is not just the boundary that is curved, but the entire volume of the mesh is made up of curved cells. However, if the cell is not adjacent to curved boundaries, it is numerically preferable to use linear cells. Thus, HOPR provides a function for uncurving curved meshes, optionally at a given distance to the boundary. The parameter nCurvedBoundaryLayers specifies the number of cells from a curved boundary (i.e. boundaries with curveIndex>0) that stay curved. For the remaining mesh, a (tri-)linear mapping using only the corner nodes is applied.

• For nCurvedBoundaryLayers=-1 the whole mesh stays curved (default).

• For nCurvedBoundaryLayers=0 in the first cell only the boundary itself remains curved, all other faces and cells in the mesh will be linear.

• For nCurvedBoundaryLayers=1-n the first n cells away from the boundary remain curved.

These choices are depicted in the figures bellow, and the table lists the scaled Jacobian ranges for the elements. The mesh becomes significantly less distorted if only the first cell is curved. Note that it is often required to curve more than the first cell, especially for fine curved boundary layer meshes.

Fig. 1.1 NACA-profile with all elements curved

Fig. 1.2 NACA-profile with only the profile boundary curved

Fig. 1.3 NACA-profile with the first cell curved

Fig. 1.4 NACA-profile with the first three cells curved

Table 1.10 Distribution of the smallest scaled Jacobians per element.

Number of elements with scaled Jacobians ranging between:	<0	<0.1	<0.2	<0.3	<0.4	<0.5	<0.6	<0.7	<0.8	<0.9	<1.0
Only boundary is curved:	0	0	0	0	8	4	8	208	100	276	1124
First element is curved:	0	0	0	0	8	4	16	208	100	288	1104
First 3 elements are curved:	0	0	0	0	16	12	32	224	92	284	1068
All elements are curved:	0	0	0	0	136	596	748	200	12	36	0

Parameter File

To test this feature, add nCurvedBoundaryLayers=n to the parameter file, which is also found in

tutorials/3-01-agglomeration_NACA/parameter.ini