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Invariant domain preserving discretization-independent schemes and convex limiting for hyperbolic systems

机译：双曲系统的不变域保持离散无关格式和凸限制

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摘要

We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by the scheme. The method is formally first-order accurate in space. Then, we introduce a series of higher-order methods. When these methods violate the invariant domain properties, they are corrected by a limiting technique that we call convex limiting. After limiting, the resulting methods satisfy all the invariant domain properties that are imposed by the user (see Theorem 7.24) and is formally high-order accurate. The two key novelties are that (i) limiting is done by enforcing bounds on quasiconcave functionals; (ii) the bounds that are enforced on the solution at each time step are necessarily satisfied by the low-order approximation. (C) 2018 Published by Elsevier B.V.
机译：我们介绍了一种非线性双曲系统的近似技术，其来源是不变的域保留。如果该方案满足基本对称性和偏对称性，则该方法与离散无关。该方法在空间上形式上是一阶准确的。然后，我们介绍了一系列高阶方法。当这些方法违反不变域属性时，将通过一种称为凸极限的限制技术对其进行校正。限制后，所得方法满足用户施加的所有不变域属性（请参见定理7.24），并且形式上是高阶准确的。这两个主要的新颖之处是：（i）通过对拟凹函数进行限制来完成限制； （ii）在每个时间步上对解决方案强制执行的界限必须通过低阶逼近来满足。 （C）2018由Elsevier B.V.发布

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