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所在平台: Udemy |
课程主页: https://www.udemy.com/course/fem-for-dummies-absolute-basics-for-cfd-multiphysics/
课程评论：没有评论
课程名称：FEM入门 - CFD与多物理场的基础知识 课程概述：有限元方法（FEM）是现代计算机辅助工程（CAE）的基石。您知道FEM也可以解决计算流体动力学（CFD）问题吗？随着工业挑战变得跨学科，基于FEM的CFD由于其轻松处理多物理场的能力，变得愈发重要。将CAE工具视为语言，FEM/变分方法则是通用“脚本”。FEM源于数学，它无缝地连接不同学科和方法。无论您是处于地质、医学、设计、化学、建筑还是更广泛的STEM领域：FEM都适合您（这门课程也是如此！）。尽管FEM通常因其繁重的数学背景而令许多人感到畏惧，但**这门课程简化了复杂性**。不需要高级数学，只需具备本科的微积分、偏微分方程和线性代数基础。 在两个小时的课程中，您将获得直观、实用的技能。具体来说，您将能够： - 使用电子表格构建FEM求解器，解决与热传导/扩散和基本流动相关的实际问题。无需编写代码，课程一步步在Excel中详细展示，让您清楚地看到每个矩阵条目和荷载向量是如何产生的。 - 驯服以对流主导的流动，使用SUPG稳定化。FEM CFD的一个挑战是准确模拟高流速问题。实现流线-上风过程/佩托-加勒金方法，实时观察矩阵结构的变化，消除解中的不物理震荡。 - 理解守恒与变分框架。守恒方程和均衡方程为您提供了正确的差分方程视角！并肩推导有限体积通量平衡和有限元弱形式，让您认识到数学基础、扩散和任意CFD软件中的传输过程。通过从头构建这些平衡，避免出现不适定的不可解方程。 - 理解基本的误差分析与收敛绘图。计算L₂误差范数，生成对数-对数收敛图，并培养验证网格细化是否提高精度的关键习惯。 额外内容：访问一个Julia脚本，它可以读取Gmsh网格，解决一维泊松和SUPG问题，并通过制造解的方法进行不同多项式阶数的网格收敛研究。这个可选模块作为通向全无结构二维纳维-斯托克斯编码的桥梁。 到课程结束时，您不仅能够建立扎实的基础来应对与FEM相关的实际工业问题，还能开始理解商业求解器背后的工作原理，使您能更好地使用黑箱，改善结果故障排除，并自信地解决更复杂的多物理场模拟问题。
**FEM is the cornerstone of modern CAE.** Did you know FEM can also tackle CFD? Absolutely! As industrial challenges become interdisciplinary, FEM-based CFD is rising in relevance due to its ability of easily handling multiphysics. Think of CAE tools as languages-FEM/variational method is the universal *script*. Rooted in mathematics, it bridges disciplines and methods seamlessly. Whether you're in geology, medicine, design, chemistry, architecture, or STEM at large: FEM is for you (and so is this course!). While FEM's math-heavy reputation intimidates many, **this course cuts through complexity**. No advanced math required-just undergrad calculus, differential equations, and linear algebra. **In two hours, you'll gain intuitive, hands-on skills to.In just two hours, you will:Build spreadsheet-powered FEM solvers for practically relevant problems like heat transfer/diffusion with reaction and basic flow problems. No coding required-everything is laid out step-by-step in Excel so you see exactly how each matrix entry and load vector arises.Tame convection-dominated flows with SUPG stabilization. One of the challenges in FEM CFD has been modelling high-speed flow problems accurately. Implement the Streamline-Upwind/Petrov-Galerkin approach, and watch the change in matrix structures in real time as it removes unphysical oscillations from your solutions.Understand both conservation and variational frameworks. Conservation equations and balance equations put the differential equations into correct perspective! Derive finite-volume flux balances and finite-element weak forms side-by-side-so you'll recognize the mathematical underpinnings, diffusion, and transport in any CFD package. Avoid ill posed unsolvable equations by constructing these balances from scratch.Understand basic error analysis & convergence plotting. Calculate L₂ error norms, generate log-log convergence plots, and develop the critical habit of verifying your mesh refinement improves accuracy.Extra Content: Access a Julia script that reads Gmsh meshes, solves 1D Poisson and SUPG problems, and runs a grid-convergence study via the Method of Manufactured Solutions across various polynomial orders. This optional module acts as a bridge towards full unstructured 2D Navier Stokes coding.By course end, you'll not only be able to build a solid foundation towards tackling practical industrially relevant problems using FEM, but also begin to understand what goes on behind the scenes of commercial solvers-empowering you to get better at using black boxes, better at troubleshooting results, as you confidently tackle more advanced multiphysics simulations.
