Mixed-order curving for viscous meshes

Linear hybrid unstructured meshes are elevated to mixed-order meshes in response to geometry curvature. The linear meshes are elevated to the required degree on an element-by-element basis in regions of high geometry curvature. Weighted condition number mesh smoothing is used to optimize the current mixed-order mesh. Periodically the mesh is tested for additional element elevation using a deviation criterion. Once the mesh smoothing is complete the mesh can be exported as a mixed order mesh or uniformly elevated to the desired degree. Details of the mesh elevation and smoothing process are described. Several three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality mixed-order meshes.