◈ 학술지
◈ 도서
◈ 전자학술지
◈ 투고요령
◈ 수학신간도서
◈ MSC
◈ 논문검색
◈ 학술행사
홈 > 학술정보 >학술행사 > 세미나
KAIST 수리과학과 세미나

Title
[응용수학 세미나] Method of moving frames to solve the shallow water equations on arbitrary rotating curved surfaces
Speaker
천세훈   (Yonsei University )
Date
2017-08-16 15:00:00
Host
KAIST
Place
(E2) Room 2214
Abstract
A novel high-order numerical scheme is proposed to solve the shallow water equations (SWEs) on arbitrary rotating curved surfaces. Based on the method of moving frames (MMF), the proposed scheme not only has the smallest dimensionality of two in space, but also does not require either of (i) metric tensors, (ii) composite meshes, or (iii) the surrounding space. The MMF-SWE formulation is numerically discretized using the discontinuous Galerkin method of arbitrary polynomial order p in space and an explicit Runge-Kutta scheme in time. In this talk, we start with the fundamental concepts of the innovational moving frames for Riemannian geometry developed by the famous French mathematician Elie Cartan in the early 20th century. Then, we discuss its adaptation and validity in the discrete space for scientific computing by overviewing the past works on conservational laws and diffusion equations. Applications to SWEs will be explained in details in views of algorithmic novelty to overcome the classical issues of PDEs on the closed surface such as geometric singularities and rotational effects. Results of six standard tests on the sphere will be displayed with the optimal order of convergence of p+1. Also, its general applicability and stability on arbitrary rotating surfaces such as ellipsoid, irregular, and non-convex surfaces will be demonstrated.
개인정보보호정책 l 이메일주소집단수집금지 l 뷰어다운로드
qr코드