arXiv subjects

Zhuyan Tang

Publications and source records attributed to Zhuyan Tang.

2 recordsLinked to original sources

arXiv2025

New Fully Discrete Active Flux Methods with Truly Multi-Dimensional Evolution Operators and WENO Reconstruction

We propose new fully discrete third-order accurate Active Flux and WENO methods based on truly multidimensional evolution operators for the two-dimensional acoustic equations. Building on the method of bicharacteristics, several approximate evolution operators are derived that yield an improved stability of the resulting schemes. A linear stability analysis is applied to determine the maximal CFL number. The schemes are tested extensively on both continuous and discontinuous problems, confirming their robustness and accurate approximation even on coarse grids.

math.NA↗

arXiv2025

Convergence analysis for a finite volume evolution Galerkin method for multidimensional hyperbolic systems

We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of gas dynamics. We show the stability and the consistency of the numerical approximations. By means of the generalized Lax equivalence principle we prove the convergence of numerical solutions to the strong solution on the lifespan.

math.NA↗