A High-Resolution Cell-Centered Lagrangian Method with a Vorticity-Based Adaptive Nodal Solver for Two-Dimensional Compressible Euler Equations (Communications in Computational Physics, 2018)
In this work, a second-order high-resolution LAgrangian method with aVorticity-based Adaptive Nodal Solver (LAVANS) is proposed to overcome the numericaldifficulty of traditional Lagrangian methods for the simulation of multidimensionalflows. The work mainly include three aspects to improve the performanceof the traditional CAVEAT-type cell-centered Lagrangian method. First, a vorticity-basedadaptive least-squares method for vertex velocity computation is proposed tosuppress nonphysical mesh distortion caused by the traditional five-point-stencil least-squaresmethod. Second, a simple interface flux modification is proposed such that thegeometry conservation law is satisfied. Third, a generalized Riemann problem solveris employed in the LAVANS scheme to achieve one-step time-space second-order accuracy.Some typical benchmark numerical tests validate the performance of the LAVANSscheme.