标题： 完全非线性凝聚-分裂模型的数值格式，来自波动力学理论 显示英文标题

标题： Numerical schemes for a fully nonlinear coagulation-fragmentation model coming from wave kinetic theory

摘要： 本文介绍了一种新的数值方法，用于研究完全非线性聚集-分裂模型，其中碰撞算子的聚集和分裂部分都是非线性的。 该模型近似了$3-$波动力学方程，这是波湍流理论中的一个关键框架，用于描述弱非线性系统中波谱的时间演化。 推导出一种隐式有限体积方案（FVS）来求解该方程。 据我们所知，这是第一个能够准确捕捉包含正向和反向能量级联的完全非线性聚集-分裂模型解的长期渐进行为的数值方案。 该方案应用于一些测试问题，结果与能量级联速率的理论预测高度一致。 我们进一步引入了一种加权 FVS 变体，以确保在不同核齐次程度下保持能量守恒。 通过理论分析建立了收敛性和一阶一致性，并通过测试案例中的实验收敛阶数进行了验证。 显示英文摘要

摘要： This article introduces a novel numerical approach for studying fully nonlinear coagulation-fragmentation models, where both the coagulation and fragmentation components of the collision operator are nonlinear. The model approximates the $3-$wave kinetic equations, a pivotal framework in wave turbulence theory governing the time evolution of wave spectra in weakly nonlinear systems. An implicit finite volume scheme (FVS) is derived to solve this equation. To the best of our knowledge, this is the first numerical scheme capable of accurately capturing the long-term asymptotic behavior of solutions to a fully nonlinear coagulation-fragmentation model that includes both forward and backward energy cascades. The scheme is implemented on some test problems, demonstrating strong alignment with theoretical predictions of energy cascade rates. We further introduce a weighted FVS variant to ensure energy conservation across varying degrees of kernel homogeneity. Convergence and first-order consistency are established through theoretical analysis and verified by experimental convergence orders in test cases.