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Full-Text Articles in Physical Sciences and Mathematics
Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method, David B. Stein, Robert D. Guy, Becca Thomases
Convergent Solutions Of Stokes Oldroyd-B Boundary Value Problems Using The Immersed Boundary Smooth Extension (Ibse) Method, David B. Stein, Robert D. Guy, Becca Thomases
Mathematics Sciences: Faculty Publications
The Immersed Boundary (IB) method has been widely used to solve fluid-structure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known two-dimensional benchmark flow for the Oldroyd-B constitutive model, and we show that the traditional IB-based scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity …
Immersed Boundary Smooth Extension (Ibse): A High-Order Method For Solving Incompressible Flows In Arbitrary Smooth Domains, David B. Stein, Robert D. Guy, Becca Thomases
Immersed Boundary Smooth Extension (Ibse): A High-Order Method For Solving Incompressible Flows In Arbitrary Smooth Domains, David B. Stein, Robert D. Guy, Becca Thomases
Mathematics Sciences: Faculty Publications
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this …