标题： 论太阳大气中的热传导：非线性扩散率无紧支集的解析解 显示英文标题

标题： On Thermal Conduction in the Solar Atmosphere: An Analytical Solution for Nonlinear Diffusivity without Compact Support

摘要： 科学界使用复杂的多物理场模拟来理解太阳、恒星和星际介质中的物理现象。 这些模拟必须与已知解进行对比以确保其有效性。 存在一些著名的测试，例如Sod激波管测试。 然而，缺乏针对非线性扩散率的测试。 这个问题在太阳大气中非常重要，因为各种事件释放的能量随后通过Spitzer热导率扩散。 目标是推导出1D、2D和3D中的非线性扩散率的解析解，允许存在非零背景值。 该解将用于设计数值求解器的测试，并研究太阳大气中的Spitzer导电性。 曾存在一个假设零背景值的理想解。 我们对该解进行了解析的一阶摄动。 一阶解首先与专用的非线性扩散求解器进行测试，之后用于对单流体和多流体辐射磁流体动力学代码Ebysus进行基准测试，该代码用于研究太阳。 理论和数值建模用于研究Spitzer导电性在纳米耀斑释放能量传输中的作用。 所得到的解析解在其有效区域内准确地模拟了非线性扩散率，并在区域外近似有效。 发现Ebysus代码中的各种数值方案正确地模拟了Spitzer导电性。 由于Spitzer导电性，代表性纳米耀斑的能量在生命的第一秒内扩散了9 Mm，这强烈依赖于电子密度。 解析的一阶解是确保太阳复杂模拟物理有效性的重要进展。 此外，由于推导和论证是通用的，它们可以轻松地被遵循以处理其他非线性扩散问题。 显示英文摘要

摘要： The scientific community employs complicated multiphysics simulations to understand the physics in Solar, Stellar, and Interstellar media. These must be tested against known solutions to ensure their validity. Several well-known tests exist, such as the Sod shock tube test. However, a test for nonlinear diffusivity is missing. This problem is highly relevant in the Solar atmosphere, where various events release energy that subsequently diffuses by Spitzer thermal conductivity. The aim is to derive an analytical solution for nonlinear diffusivity in 1D, 2D, and 3D, which allows for a nonzero background value. The solution will be used to design a test for numerical solvers and study Spitzer conductivity in the Solar atmosphere. There existed an ideal solution assuming zero background value. We perform an analytical first-order perturbation of this solution. The first-order solution is first tested against a dedicated nonlinear diffusion solver, whereupon it is used to benchmark the single- and multifluid radiative magnetohydrodynamics code Ebysus, used to study the Sun. The theory and numerical modeling are used to investigate the role of Spitzer conductivity in the transport of energy released in a nanoflare. The derived analytical solution models nonlinear diffusivity accurately within its region of validity and approximately beyond. Various numerical schemes in the Ebysus code have been found to model Spitzer conductivity correctly. The energy from a representative nanoflare has been found to diffuse 9 Mm within the first second of its lifetime due to Spitzer conductivity alone, strongly dependent on the electron density. The analytical first-order solution is a step forward in ensuring the physical validity of intricate simulations of the Sun. Additionally, since the derivation and argumentation are general, they can easily be followed to treat other nonlinear diffusion problems.