這是一個由學生報告的討論班，主題是黏彈流的計算課題。
黏彈流(Viscoelastic fluid flow) 是一種複雜流體，是描述高分子流(polymeric fluid flow)的偏微分方程模型。此模型的一個參數是彈性黏性比，稱作Weisenberg 數。在黏彈流計算的一個困難是: High Weissenberg Number Problem (HWNP), 是說當Weissenberg number 大時，現有的計算方法都不穩定。這是一個值得挑戰的科學計算課題。我打算讓學生閲讀相關的文獻，並進行相關的研究。相關文獻如下:
1. Projection methods for incompressible Navier-Stokes equations,
Bell-Colella, Glaz, Second-order Projection method (1989),
Wei-Nan E and Jian-Guo Liu, Projection method-I (1995)
2. Trangenstein and Colella, A High-order Godunov method for modeling finite deformation in elastic-plastic solids (1991), CPAM
3. Miller and Colella, A High-order Godunov method for elastic-plastic solids (2001) JCP
4. Nonaka, Trebotich, Miller, Graves, Colella, A higher-order upwind method for viscoelastic flow (2009) Comm Appl. Math. And Comp. Sci.
5. Niethammer, Marsehall, Kunkelmann and Bothe, A numerical stabilization framework for viscoelastic fluid flow using finite volume method on general unstructured meshes (2017)
6. Jiang, Schroeder, Selle, Teran, Stomakhin, The affine particle-in-cell method