Second order symmetry-preserving conservative intersection-based remapping method in two-dimensional cylindrical coordinates

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The importance of preserving physical symmetry in arbitrary Lagrangian-Eulerian (ALE) simulations is well recognized. In the past decades, first order spherical-symmetry-preserving Lagrangian and ALE methods in two-dimensional cylindrical coordinates were developed. And there are also several works about second order spherical-symmetry-preserving cell-centered Lagrangian schemes. The goal of this paper is to develop Second order spherical-symmetry-preserving intersection-based remapping method in two-dimensional cylindrical coordinates. The method is capable to preserve one-dimensional spherical symmetry when the old grid is equiangular polar mesh and the rezoning algorithm only moves points in the radial directions by the same amount for all points with the same spherical radius. The remapping method has second order accuracy almost uniformly (the accuracy drops to first order close to the revolution axis), has good properties such as conservation for mass, momentum and total energy. The symmetry-preserving property and second order accuracy of our new remapping method are proved mathematically and demonstrated by several numerical examples.