论文标题
部分可观测时空混沌系统的无模型预测
Benchmarks for infinite medium, time dependent transport problems with isotropic scattering
论文作者
论文摘要
广泛使用的AZURV1运输基准包装为各种初始条件提供了一系列各向同性散射问题的解决方案（Ganapol 2001）。这些解决方案中的大多数具有初始条件，该条件是空间中的Dirac Delta功能。结果，这些基准是在计算机代码中用于验证测试的挑战性问题。然而，在模拟中近似Delta函数通常会导致较低的收敛顺序和无法测试高阶数值方法的收敛性。尽管在文献中有一些示例将这些解决方案集成为Green的运输运营商的功能，以便为更容易模拟的来源产生结果，但它们的范围有限，并简要解释了。对于初始条件和来源的采样，我们提出了未填充和相撞的标量通量的解决方案，以促进数值求解器中源处理的准确测试。对于某些来源，以分析形式发现了未填充标量通量的解决方案。由于整合绿色的功能通常是不平凡的，因此包括对整合难度的讨论和解决融合积分的解决方案。此外，我们未完成的解决方案可以用作验证研究中的源术语，其方式与制造解决方案的方法类似。
The widely used AZURV1 transport benchmarks package provides a suite of solutions to isotropic scattering transport problems with a variety of initial conditions (Ganapol 2001). Most of these solutions have an initial condition that is a Dirac delta function in space; as a result these benchmarks are challenging problems to use for verification tests in computer codes. Nevertheless, approximating a delta function in simulation often leads to low orders of convergence and the inability to test the convergence of high-order numerical methods. While there are examples in the literature of integration of these solutions as Green's functions for the transport operator to produce results for more easily simulated sources, they are limited in scope and briefly explained. For a sampling of initial conditions and sources, we present solutions for the uncollided and collided scalar flux to facilitate accurate testing of source treatment in numerical solvers. The solution for the uncollided scalar flux is found in analytic form for some sources. Since integrating the Green's functions is often nontrivial, discussion of integration difficulty and workarounds to find convergent integrals is included. Additionally, our uncollided solutions can be used as source terms in verification studies, in a similar way to the method of manufactured solutions.
