The prediction of long-term dynamics of transitional environments, e.g., lagoon evolution, salt-marsh growth or river delta progradation, is an important issue to estimate the potential impacts of different scenarios on such vulnerable intertidal morphologies. The numerical simulation of the combined accretion and consolidation, i.e., the two main processes driving the dynamics of these environments, however, suffers from a significant geometric non-linearity, which may result in a pronounced grid distortion using standard grid-based discretization methods. The present work describes a novel numerical approach, based on the Virtual Element Method (VEM), for the long-term simulation of the vertical dynamics of transitional landforms. The VEM is a grid-based variational technique for the numerical discretization of Partial Differential Equations (PDEs) allowing for the use of very irregular meshes consisting of a free combination of different polyhedral elements. The model solves the groundwater flow equation, coupled to a geomechanical module based on Terzaghi's principle, in a large-deformation setting, taking into account both the geometric and the material non-linearity. The use of the VEM allows for a great flexibility in the element generation and management, avoiding the numerical issues connected with the adoption of strongly distorted meshes. The numerical model is developed, implemented and tested in real-world examples, showing an interesting potential for addressing complex environmental situations.

过渡环境长期动态的预测，例如泻湖的演变，盐沼的增长或河三角洲的发展，是评估不同情景对这种脆弱的潮间带形态潜在影响的重要问题。组合的吸积和固结（即驱动这些环境动力学的两个主要过程）的数值模拟具有明显的几何非线性，使用基于标准网格的离散化方法可能会导致明显的网格失真。本工作描述了一种基于虚拟元素方法（VEM）的新型数值方法，用于长期模拟过渡地貌的垂直动力学。VEM是基于网格的变分技术，用于偏微分方程（PDE）的数值离散化，允许使用由不同多面体元素的自由组合组成的非常不规则的网格。该模型在考虑到几何和材料非线性的情况下，在大变形条件下求解地下水流量方程，并结合基于Terzaghi原理的地质力学模块。VEM的使用为元素生成和管理提供了极大的灵活性，避免了与采用严重扭曲的网格有关的数值问题。该数值模型是在实际示例中开发，实施和测试的，显示了解决复杂环境状况的有趣潜力。