A third-order multi-moment cell-centered Lagrangian scheme for hydrodynamics with an accurate 2D nodal solver

TL;DR

This paper introduces a high-order cell-centered Lagrangian scheme for 2D hydrodynamics that combines multi-moment finite volume methods with a novel 2D nodal Riemann solver, enhancing accuracy and stability.

Contribution

The paper develops a new high-order Lagrangian scheme integrating MCV with a 2D Riemann solver based on EUCCLHYD, featuring innovative jump and balance conditions for improved accuracy and robustness.

Findings

The scheme achieves high-order accuracy in 2D hydrodynamics simulations.

Numerical experiments confirm the robustness and stability of the proposed method.

Abstract

This paper presents a novel high-order cell-centered Lagrangian scheme for 2D compressible hydrodynamics by bridging the multi-moment constrained finite volume method (MCV) [16, 51, 52] with a nodal Riemann solver. This scheme (denoted by LMCV) not only maintains high-order accuracy as MCV but also inherits the conservation and robust properties of the nodal Riemann solver. On the one hand, the MCV employs and evolves both the point-values (PV) at cell vertexes and the volume-integrated averages (VIA) on computational mesh, which ensures the rigorous numerical conservation and establishes an adequate foundation for the computation of Lagrangian fluxes with high accuracy. On the other hand, we developed a 2D Riemann solver based on EUCCLHYD [24], it takes fully advantage of numerical formulations from high-order scheme and accomplishes the compatibility between the mesh movement and numerical fluxes. The main new features of the solver are the introduction of a new set of jump and balance conditions. The jump condition provides a high-accurate formulation linking the surface pressure of each cell to its nodal velocity, while the balance condition ensures nodal conservation and stabilizes the velocity field without losing accuracy. More intriguing is that our nodal solver can be regarded as a natural high-order extension of the HLLC and the HLLC-2D [41] solvers. The comparison between these solvers better demonstrates our innovative approach in addressing the difficulties encountered in constructing 2D high-order Lagrangian schemes. A variety of numerical experiments are carried out to illustrate the accuracy and robustness of the algorithm.