The classical Lagrangian approach will lead to infinite deformation of meshes, especially for viscous flows. In this paper, we will use the unified coordinate system approach to compute viscous flows. This approach, invented by Hui and his coworkers, contains an inner parameter leading to a continuous switch between the classical Lagrangian approach and Eulerian approach. Severe grid deformation can be avoided by controlling this inner parameter.
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Hui, W.H., Wu, Z.N. & Gao, B. Preliminary Extension of the Unified Coordinate System Approach to Computation of Viscous Flows. J Sci Comput 30, 301–344 (2007). https://doi.org/10.1007/s10915-006-9096-6
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DOI: https://doi.org/10.1007/s10915-006-9096-6