A cell-centered indirect Arbitrary-Lagrangian-Eulerian discontinuous Galerkin scheme on moving unstructured triangular meshes with topological adaptability.

• An indirect ALE DG model on moving triangular meshes with mesh topological adaptability is developed. • The best features of the Lagrangian description, DG method and adaptive topology optimization strategy are incorporated. • The present scheme can handle hydrodynamics problems which involve complex deformations, large distortions and strong shock. • The new indirect ALE DG scheme is more accurate and stable than the conventional Lagrangian DG scheme. In this paper, we present a novel cell-centered indirect Arbitrary-Lagrangian-Eulerian (ALE) discontinuous Galerkin (DG) scheme on moving unstructured triangular meshes with mesh topological adaptability, aiming to deal with the strong distortions and large deformation flow problems. The scheme combines the explicit time marching Lagrangian DG methodology with the adaptive mesh topology optimization technique. The scheme consists of the following three steps. Firstly, we utilize the Runge-Kutta DG method to solve the compressible Euler equation in Lagrangian framework, and employ a nodal solver to obtain the nodal velocity and numerical fluxes across element boundaries. The physical variable and nodal position are updated in this step. Secondly, the adaptive mesh topology optimization technique, which includes the mesh refinement, edge collapse operation and mesh regularization, is implemented to eliminate the highly distorted elements and improve the mesh quality. Thirdly, the conservative remapping algorithm is employed, which can maintain the conservative interpolation of the Lagrangian solution onto the remeshed grid. The present indirect ALE DG scheme can ensure the high quality of the mesh by optimizing the topology connectivity, so that the present scheme can successfully simulate complex vortical flow problems for a sufficient simulation time. Due to the inherent Lagrangian nature, the present scheme can naturally track the multi-material flow interface, rather than using algorithms with interface reconstruction or diffuse interfaces. The scheme is validated with several benchmark flow problems. It is demonstrated that the present indirect ALE DG scheme with topological adaptability can accurately simulate flow problems with large fluid deformations and distortions. It can achieve remarkable improvements compared with the conventional Lagrangian DG method with fixed topological connectivity. [ABSTRACT FROM AUTHOR]