High-Order Cell-Centered Lagrangian Spectral Volume Method on Curvilinear Meshes (Communications in Computational Physics, 2025)
This paper introduces a novel high-order, cell-centered Lagrangian methodtailored for curvilinear meshes. To ensure stable curvilinear mesh motions and avoidthe algorithmic complexity associated with special mesh stabilization techniques, thismethod exploits the subcell-wise computational degrees of freedom inherent in thewell-established spectral volume (SV) method. It is demonstrated that the numerical results obtained from the SV reconstruction can serve as direct inputs for nodalsolvers, yielding favorable mesh node velocities. For cells potentially containing discontinuities, the classical finite volume (FV) reconstruction is applied to each subcellwithin these cells instead. This subcell-wise reconstruction, analogous to commoncell-wise limitations or reconstructions, can effectively reduce unphysical oscillations.More importantly, it is capable of suppressing spurious mesh motions following thesame principle of not introducing stabilization techniques such as input correction.The proposed Lagrangian method is completely designed in the computational spacewith transformed governing equations. Hence, both of the aforementioned SV andFV reconstructions can be performed with the same ease as on uniform and time-independent Eulerian meshes and achieve high-order accuracy. The method furtherbenefits from simplicity and uniformity in its implementation, the compactness of thereconstruction formulae utilized, and the efficiency of the iteration-free nodal solveremployed. It exhibits consistently satisfying performance across various numericaltests, including those involving significant mesh deformation and extreme conditionssuch as low-pressure states accompanied by strong shocks.
Keywords: Lagrangian gas dynamics; high-order method; curvilinear mesh; spectral volume