Серия лекций Prof. Chi-Wang Shu "High order schemes for convection dominated problems"

Название серии: “High order schemes for convection dominated problems”

Профессор Чи-Ванг Шу работает на кафедре прикладной математики вУниверситете Брауна в США ( Brown University ) и известен своими работами в области вычислительной аэродинамики (схемы ENO / WENO / RKDG ), численного решения гиперболических законов сохранения и уравнений Гамильтона-Якоби. Он является одним из наиболее цитируемых авторов по версии   ISI Web of Knowledge . Предоставляется уникальная возможность прослушать лекции и пообщаться с этим выдающимся ученым и замечательным человеком.


Convection dominated partial differential equations are used extensively in applications including fluid dynamics, astrophysics, electro-magnetism, semi-conductor devices, and biological sciences. High order accurate numerical methods are efficient for solving such partial differential equations, however they are difficult to design because solutions may contain discontinuities and other singularities or sharp gradient regions. In this series of lectures we will give a general survey of several types of high order numerical methods for such problems, including weighted essentially non-oscillatory (WENO) finite difference methods, WENO finite volume methods, and discontinuous Galerkin (DG) finite-element methods. We will discuss essential ingredients, properties and relative advantages of each method, and comparisons among these methods. Recent development and applications of these methods will also be discussed.

 


Lecture 1: 19 сентября:
Место 119 ГК МФТИ
Время 16:00

WENO finite volume and finite difference schemes
The following topics will be discussed:

  1. Setup of finite volume framework
  2. WENO reconstruction
  3. Time discretization
  4. Multi-dimensions and unstructured meshes
  5. Setup of conservative finite difference framework
  6. Relationship between finite difference and finite volume schemes
  7. Recent development and applications:
    1. Inverse Lax-Wendroff type boundary treatments
    2. Free-stream preserving finite difference schemes on curvilinear meshes
    3. A homotopy method based on WENO schemes for solving steady state problems
    4. Application: Shock-vortex and vortex-vortex interactions

Lecture 2: 20 сентября:
Место 119 ГК МФТИ
Время 15:00

DG method I: hyperbolic conservation laws

  1. The first DG scheme in 1973 for neutron transport
  2. Setup of Runge-Kutta DG schemes
  3. Properties of DG schemes
  4. Systems and multi-dimensions, unstructured meshes
  5. Remarks on implementations: matrix form for linear equations, quadratures and quadrature-free, CPR schemes
  6. Recent development and applications:
    1. A simple WENO limiter for DG schemes
    2. Positivity-preserving DG and finite volume schemes
    3. DG method for problems involving delta-singularities

Lecture 3: 23 сентября:
Место Климентовский пер. д.1 стр.1
Время 11:00 (возможны изменения, следите за новостями)

DG method II: PDEs with higher order derivatives

  1. Convection-diffusion equations: the local DG (LDG) scheme
  2. Other types of DG discretizations for diffusion
  3. Convection-dispersion equations (KdV equations)
  4. Higher order PDEs
  5. Recent development and applications:
    1. Positivity-preserving second order DG method on general triangulations
    2. Multiscale DG method for solving elliptic problems with curvilinear unidirectional rough coefficients
    3. Energy conserving LDG methods for second order wave equations