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A community benchmark for viscoplastic thermal convection in a 2-D square box

机译：二维方箱中粘塑性热对流的社区基准

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摘要

Numerical simulations of thermal convection in the Earth's mantle often employ a pseudoplastic rheology in order to mimic the plate-like behavior of the lithosphere. Yet the benchmark tests available in the literature are largely based on simple linear rheologies in which the viscosity is either assumed to be constant or weakly dependent on temperature. Here we present a suite of simple tests based on nonlinear rheologies featuring temperature, pressure, and strain rate-dependent viscosity. Eleven different codes based on the finite volume, finite element, or spectral methods have been used to run five benchmark cases leading to stagnant lid, mobile lid, and periodic convection in a 2-D square box. For two of these cases, we also show resolution tests from all contributing codes. In addition, we present a bifurcation analysis, describing the transition from a mobile lid regime to a periodic regime, and from a periodic regime to a stagnant lid regime, as a function of the yield stress. At a resolution of around 100 cells or elements in both vertical and horizontal directions, all codes reproduce the required diagnostic quantities with a discrepancy of at most approximate to 3% in the presence of both linear and nonlinear rheologies. Furthermore, they consistently predict the critical value of the yield stress at which the transition between different regimes occurs. As the most recent mantle convection codes can handle a number of different geometries within a single solution framework, this benchmark will also prove useful when validating viscoplastic thermal convection simulations in such geometries.
机译：为了模拟岩石圈的板状行为，地幔热对流的数值模拟通常采用假塑性流变学。然而，文献中提供的基准测试很大程度上是基于简单的线性流变学，在该流变学中，粘度被认为是恒定的或弱依赖于温度的。在这里，我们提出了一套基于非线性流变的简单测试，这些非线性流变具有温度，压力和应变率相关的粘度。基于有限体积，有限元或光谱方法的11种不同代码已用于运行5个基准情况，从而导致二维方盒中的盖子，移动盖子和周期性对流。对于其中两种情况，我们还显示了所有贡献代码的分辨率测试。此外，我们提出了分叉分析，描述了根据屈服应力从活动盖状态过渡到周期性状态，以及从周期性盖状态过渡到停滞盖状态的过程。在垂直和水平方向上具有约100个单元或元素的分辨率时，所有代码均在线性和非线性流变同时存在的情况下，再现所需的诊断量，且差异最多约为3％。此外，他们始终预测屈服应力的临界值，在该屈服应力的临界点处会发生不同状态之间的过渡。由于最新的地幔对流代码可以在一个解决方案框架内处理许多不同的几何形状，因此在验证此类几何形状的粘塑性热对流模拟时，该基准也将非常有用。

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