论文标题
阳性 - 具有$Δ\的双曲线系统的数值方案， - $冲击解决方案及其收敛分析
Positivity--preserving numerical scheme for hyperbolic systems with $δ\,-$ shock solutions and its convergence analysis
论文作者
论文摘要
戈杜诺夫（Godunov）类型的双曲线系统类型数值方案，提出了非古典$δ-$ shocks。结果表明，数值近似收敛到溶液并保留系统的物理特性，例如正密度和有界速度。该方案已通过使用适当的斜率限制器扩展到阳性保存和速度结合的二阶准确方案。将数值结果与现有文献进行了比较，并且该方案被证明可以有效地捕获解决方案。该论文提出了一个双曲线系统，该系统通过将系统的适当分离为两种标量保护定律而构建了熵满足方案，并具有不连续的通量。
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $δ-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the system such as positive density and bounded velocity. The scheme has been extended to positivity preserving and velocity bound preserving second-order accurate scheme by using appropriate slope limiters. The numerical results are compared with the existing the literature and the scheme is shown to capture the solution efficiently. The paper presents a hyperbolic system, for which an entropy satisfying scheme is constructed through an appropriate decoupling of the system into two scalar conservation laws with discontinuous flux.
