论文标题
针对参数依赖性线性双曲线保护法的有限体积解决方案的重建
Reconstruction of finite volume solution for parameter-dependent linear hyperbolic conservation laws
论文作者
论文摘要
本文涉及开发合适的数值方法，用于近似参数依赖性线性双曲线保护法的不连续解。目的是从任何时间的新实例中重建此类近似，从对新参数值的溶液轨迹的预计快照的转换转换。在有限的体积设置中，提出了一种从重建 - 进化平均水平的Godunov的方法中启发的重建 - 转化平均水平（RTA）算法。它允许在三个步骤中执行通过分段恒定重建的快照的转换。该方法已完全详细介绍并分析用于求解参数依赖的传输方程，该方程与该问题有关，该方程与问题的特征性固有性有关。传输方程和线性弹性动力学方程的数值结果说明了所提出的方法的良好行为。
This paper is concerned with the development of suitable numerical method for the approximation of discontinuous solutions of parameter-dependent linear hyperbolic conservation laws. The objective is to reconstruct such approximation, for new instances of the parameter values for any time, from a transformation of pre-computed snapshots of the solution trajectories for new parameter values. In a finite volume setting, a Reconstruct-Transform-Average (RTA) algorithm inspired from the Reconstruct-Evolve-Average one of Godunov's method is proposed. It allows to perform, in three steps, a transformation of the snapshots with piecewise constant reconstruction. The method is fully detailed and analyzed for solving a parameter-dependent transport equation for which the spatial transformation is related to the characteristic intrinsic to the problem. Numerical results for transport equation and linear elastodynamics equations illustrate the good behavior of the proposed approach.
