反应性沉降模型的不变区域保持高阶格式
Invariant-region-preserving high-order schemes for a model of reactive sedimentation
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中文总结 AI 辅助
本文为反应性沉降模型提出高阶有限体积格式，采用MUSCL和CWENO3重构及SSPRK时间离散，在零扩散下保持不变区域性质，并模拟二次沉淀池反硝化验证性能。
中文摘要 AI 辅助
由生物和惰性固体物质以及液体底物组成的混合物的反应性沉降，通过一个对流-扩散-反应方程组进行建模。在此过程中，分散在粘性流体中的小固体颗粒因重力而沉降，同时固体与液体组分（底物）之间发生化学反应。在反应性沉降过程的应用中，主要用途是在水资源回收设施（WRRFs）中模拟和控制二次沉淀池（SSTs）。控制方程包括一个用于固体总浓度的非线性强退化抛物型方程，以及包含固体组分和底物反应项的输运方程。为了精确逼近模型方程，开发了一种使用多项式重构的高阶有限体积格式。使用了两种重构方法：二阶单调上游中心格式（MUSCL）和三阶中心加权本质无振荡（CWENO3）方法。此外，对于时间离散化，我们采用二阶和三阶的强稳定性保持龙格-库塔（SSPRK）格式。CWENO3格式辅以限制器，在零扩散情况下，所设计的高阶格式被证明保持不变区域性质。该性质尤为重要，因为它确保在每个时间迭代中获得物理相关的数值解。此外，提出了扩散项的高阶逼近以逼近完整的模型方程。在WRRFs中连续运行条件下SSTs中反硝化的模拟展示了模型及其离散化的性能。最后，收敛性测试显示了所开发格式的精度阶数和不变区域保持性。
英文摘要
Reactive sedimentation of mixtures composed by biological and inert solid matter including liquid substrates is modelled by a system of convection-diffusion-reaction equations. In this process, the small solid particles dispersed in the viscous fluid settle due to gravity while simultaneous chemical reactions take place between solid and liquid components (substrates). Among the applications of reactive sedimentation processes, the principal use is in the simulation and control of secondary settling tanks (SSTs) in water resource recovery facilities (WRRFs). The governing equations include a nonlinear strongly degenerate parabolic equation for the total concentration of solids, and transport equations including reaction terms for the solid components and substrates. To accurately approximate the model equations, a high-order finite volume scheme is developed using polynomial reconstructions. Two reconstruction methods are used, a second-order monotonic upstream-centered scheme (MUSCL), and a third-order central weighted essentially non-oscillatory (CWENO3) method. In addition, for the time discretization, we employ strong stability preserving Runge-Kutta (SSPRK) schemes of second- and third-order. The CWENO3 scheme is complemented with limiters, and in the case of zero diffusion, the designed high-order schemes are shown to preserve an invariant-region property. This property is particularly relevant as it ensures that physically relevant numerical solutions are obtained at each time iteration. In addition, high-order approximations for the diffusion terms are proposed to approximate the complete model equations. Simulations of denitrification in SSTs under a continuously operated regime in WRRFs demonstrate the performance of the model and its discretization. Finally, convergence tests show the order of accuracy of the developed scheme and the invariant-region preservation.
发表机构
- Universidad del Bío-Bío（比奥比奥大学）
- Universidad de Aysén（艾森大学）
- University of Groningen（格罗宁根大学）
- Universidad de Concepción（康塞普西翁大学）
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