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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Well-balanced positivity-preserving high-order discontinuous Galerkin methods for Euler equations with gravitation
引力 欧拉方程 高阶间断 Galerkin方法
2023/11/29
We develop high order discontinuous Galerkin (DG) methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. Such problems may yield steady-state solutions and the density and p...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：No blow-up by nonlinear It? noise for the Euler equations
非线性 爆炸 欧拉方程 噪声
2023/5/17
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
平滑数据 二维布西内斯 三维欧拉方程 稳定近似 自相似爆炸
2023/4/13
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Uniqueness of BV Solution for Compressible Euler Equations
可压缩 欧拉方程 BV解 唯一性
2023/4/17
Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conser...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions for a free boundary problem of 3-D compressible Euler equations coupled with a nonlinear Poisson equation
三维 可压缩欧拉方程 耦合 非线性泊松方程 自由边界问题 稳定性条件
2023/4/18
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Finding solutions to the multi-dimensional compressible Euler equations
多维 可压缩 欧拉方程 解
2023/4/24
This talk will survey some results for the two- or three-space dimensional compressible Euler equations. We shall present non-uniqueness results of weak entropy solutions using convex integration and ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A constructive proof of finite time blowup of 3D incompressible Euler equations with smooth data
光滑数据 三维不可压缩 欧拉方程 有限时间爆破 构造性证明
2023/5/10
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a ...
Non-Oscillatory Central Schemes for the Incompressible 2D Euler Equations
Hyperbolic conservation laws second-order accuracy central difference schemes non-oscillatory schemes Incompressible Euler equations
2015/10/8
We adopt a non-oscillatory central scheme, first presented in the context of Hyperbolic conservation laws in [nessyahu-tadmor] followed by [jiang-tadmor], to the framework of the incompressible Eule...
Application of High-Order Energy Stable Flux Reconstruction Schemes to the Euler Equations
High-Order Energy Stable Flux Reconstruction Schemes Euler Equations
2015/7/3
The authors recently identified an infinite range of high-order energy stable flux reconstruction (FR) schemes in 1D and on triangular elements in 2D. The new flux reconstructi...
A Conservative Meshless Scheme: General Order Formulation and Application to Euler Equations
Conservative Meshless Scheme General Order Formulation Application Euler Equations
2015/7/3
In this paper, we present a mesh-free, finite-volume-like scheme designed for numerically solving conservation laws. We first derive a conservative formulation for computing mesh-free @...
A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes
Multigrid methods Newton–Krylov methods Euler equations
2015/7/3
Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited,...
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
High-order conservation laws unstructured grids spectral difference spectral collocation method Euler equations.
2015/7/2
An efficient, high-order, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of struc...
How Many Steps are Required to Solve the Euler Equations of Steady,Compressible Flow:In Search of a Fast Solution Algorithm
Euler Equations Compressible Flow:Search Fast Solution Algorithm
2015/7/2
New versions of implicit algorithms are proposed for the efficient solution of the Euler equations of com pressible flow. The methods are based on a pre conditioned, Lower-Upper (LU) implem...
Gas-Kinetic Relaxation (BGK-Type) Schemes for the Compressible Euler Equations
Gas-Kinetic Relaxation (BGK-Type) Schemes Compressible Euler Equations
2015/7/1
Starting from the gas-kinetic model, a new class of relaxation schemes for the Euler equations are presented. Instead of linerizing the Euler equa-tions into a few simple waves, the new flow solvers a...
A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
Godunov-type scheme generalized Riemann problem Riemann problem
2014/9/26
The paper proposes and implements a third-order accurate direct Eulerian gen-eralized Riemann problem (GRP) scheme for one- and two-dimensional (1D & 2D)
Euler equations in gas dynamics. It is an ext...