Abstract Electron radiation belts are regions surrounding Earth, filled with highly energetic electrons and overlapping the majority of satellite orbits. Their multi-scale and rapidly evolving dynamics are modelled by the mean of a diffusion equation involving a highly anisotropic and inhomogeneous diffusion tensor. Finite difference based methods have been the preferred method of discretization in physical codes, starting from ONERA’s Salammbo-Electron model, the pioneering 3-dimensional code in the radiation belts community. This choice however does not prevent several numerically induced constraints impacting the reliability of the code as well as its computational cost. Thus in this paper we present the outcome of our investigation to improve Salammbo’s numerical core. In particular, we present our special diffusion frame and its numerically induced limitations on our finite difference based scheme. Then we test potential alternative finite volume schemes with physically relevant properties and we finally highlight with a real case simulation the contribution of the positivity preserving scheme to evaluate the impact of cross diffusion.

中文翻译：

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电子辐射带动态代码的高各向异性扩散建模

摘要 电子辐射带是环绕地球的区域，充满高能电子并与大部分卫星轨道重叠。它们的多尺度和快速演化的动力学通过扩散方程的平均值进行建模，该方程涉及高度各向异性和非均匀扩散张量。基于有限差分的方法一直是物理代码离散化的首选方法，从 ONERA 的 Salammbo-Electron 模型开始，这是辐射带社区中开创性的 3 维代码。然而，这种选择并不能阻止影响代码可靠性及其计算成本的几个数值诱导约束。因此，在本文中，我们展示了我们为改进 Salammbo 数值核心而进行的调查结果。特别是，我们展示了我们的特殊扩散框架及其对基于有限差分的方案的数值限制。然后，我们测试具有物理相关特性的潜在替代有限体积方案，最后我们通过真实案例模拟强调了正性保持方案对评估交叉扩散影响的贡献。