标题： 符合和非等温达西-福希海默流的不连续离散化 显示英文标题

标题： Conforming and discontinuous discretizations of non-isothermal Darcy-Forchheimer flows

摘要： 我们在一个统一的框架下提出并分析了两种用于数值离散化Darcy-Forchheimer流体流动模型与描述流体温度分布的对流扩散方程耦合的方案。 第一种方法基于完全不连续的Galerkin离散化空间。 相比之下，在第二种方法中，速度在Raviart-Thomas空间中进行近似，而压力和温度仍然为分片不连续。 为处理问题的非线性，提出了一种固定点线性化策略，该策略自然地诱导出一种迭代分裂求解方法。 我们进行了统一的稳定性分析，并在问题数据的温和要求下证明了迭代算法的收敛性。 我们展示了一组广泛二维和三维的模拟，以评估误差衰减并展示所提出方法在物理上合理的测试案例中的实际性能。 显示英文摘要

摘要： We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first approach is based on fully discontinuous Galerkin discretization spaces. In contrast, in the second approach, the velocity is approximated in the Raviart-Thomas space, and the pressure and temperature are still piecewise discontinuous. A fixed-point linearization strategy, naturally inducing an iterative splitting solution, is proposed for treating the nonlinearities of the problem. We present a unified stability analysis and prove the convergence of the iterative algorithm under mild requirements on the problem data. A wide set of two- and three-dimensional simulations is presented to assess the error decay and demonstrate the practical performance of the proposed approaches in physically sound test cases.