双曲型守恒律的保界时间积分方法
Bounds Preserving Temporal Integration Methods for Hyperbolic Conservation Laws
摘要：
在这项工作中，我们提出了一个修改的显式龙格-库塔时间积分计划，保证保存任何本地定义的拟凸集的解决方案的界限。这些计划的基础上操作的双射映射之间的容许集的解决方案和真正的域严格执行的界限。在这个框架内，我们表明，它是可能的恢复范围广泛的方法独立的空间离散化，包括正性保持，离散最大值原理满足，熵耗散，不变域保持计划。此外，这些计划被证明是恢复的顺序的基础龙格-库塔法，他们是建立在准确性。额外的计算成本是两个非线性映射，通常有封闭形式的解决方案的评价。我们在数值实验中使用伪谱空间离散，没有任何显式的冲击捕获计划的非线性双曲型问题的不连续性，这种方法的实用性。
英文摘要：
In this work, we present a modification of explicit Runge-Kutta temporal integration schemes that guarantees the preservation of any locally-defined quasiconvex set of bounds for the solution. These schemes operate on the basis of a bijective mapping between an admissible set of solutions and the real domain to strictly enforce bounds. Within this framework, we show that it is possible to recover a wide range of methods independently of the spatial discretization, including positivity preserving, discrete maximum principle satisfying, entropy dissipative, and invariant domain preserving schemes. Furthermore, these schemes are proven to recover the order of accuracy of the underlying Runge-Kutta method upon which they are built. The additional computational cost is the evaluation of two nonlinear mappings which generally have closed-form solutions. We show the utility of this approach in numerical experiments using a pseudospectral spatial discretization without any explicit shock capturing schemes for nonlinear hyperbolic problems with discontinuities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
