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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...
High-Order Flux Reconstruction Schemes with Minimal Dispersion and Dissipation
High-order · Flux reconstruction Discontinuous Galerkin dispersion Dissipation Wave propagation Mathematics Subject Classifi cati
2015/7/3
Modal analysis of the flux reconstruction (FR) formulation is performed to obtain the semi-discrete and fully-discrete dispersion relations, using which, the wave properties of physical as well ...
Nodal Points and the Nonlinear Stability of High-Order Methods for Unsteady Flow Problems on Tetrahedral Meshes
Nodal Points Nonlinear Stability High-Order Methods Unsteady Flow Problems Tetrahedral Meshes
2015/7/3
High-order methods have the potential to efficiently generate accurate solutions to fluid dynamics problems of practical interest. However, high-order methods are less robust than lower-or...
Convergence Acceleration of High Order Numerical Simulations using a Hybrid Spectral Di
Numerical Algorithms Computational Fluid Dynamics Spectral Di
2015/7/3
The goal of this paper is to show how numerical simulations of uid ow using high order methods for unstructured meshes can be sped up using a hybrid multigrid method. In our work we accelerate the ste...
Advances in Bringing High-order Methods to Practical Applications in Computational Fluid Dynamics
Advances Bringing High-order Methods Practical Applications Computational Fluid Dynamics
2015/7/3
Following pioneering research by mathematicians such as Lax and Godunov, the early development of computational uid dynamics (CFD) between 1970 and 1995 was particularly pursued in the Aerospace Commu...
Efficient Relaxation Methods for High-Order Discretization of Steady Problems
Efficient Relaxation Methods High-Order Discretization Steady Problems
2015/7/3
We review the current status of solution methods for nonlinear systems arising from high-order discretization of steady compressible ow problems.
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...
Unsteady Adjoint Method for the Optimal Control of Advection and Burger’s Equations using High-Order Spectral Difference Method
Unsteady Adjoint Method Optimal Control Advection Burger’s Equations High-Order Spectral
2015/7/3
In this study, we investigate the method for adjoint-based optimal control of linear and non-linear equations. In particular, we are interested in the formulation of the unsteady adjoint method based ...
FLOW INDUCED CYLINDER OSCILLATION AND ITS CONTROL WITH HIGH ORDER SPECTRAL DIFFERENCE METHOD ON DEFORMABLE MESH
SPECTRAL DIFFERENCE METHOD DEFORMABLE MESH
2015/7/3
In the recent work by the authors, high order spectral difference (SD) method has been formulated in a framework with dynamic deformable meshes, and been demonstrated to preserve the design accuracy o...
A High-Order Spectral Difference Method for Fluid-Structure Interaction on Dynamic Deforming Meshes
High-Order Spectral Diff erence Method Fluid-Structure Interaction Dynamic Deforming Meshes
2015/7/3
In previous work by the authors, Spectral Difference Method has been formulated in a framework with time-dependent moving deformable meshes. The framework has also been shown to preserve the des...
High-Order Numerical Algorithms for Steady and Unsteady Simulation of Viscous Compressible Flow with Shocks
Steady Unsteady Simulation
2015/6/18
Theoretical developments of flux reconstruction method
Unstructured high-order methods
The Flux Reconstruction approach
Energy Stable Flux Reconstruction schemes
Flux Reconstruction as Filtere...
High-order fundamental and general solutions of convection-diffusion equation and their applications with boundary particle method
High-order fundamental solution High-order general solution Boundary particle method Radial basis function Meshfree Multiple reciprocity-BEM
2010/10/22
In this study, we presented the high-order fundamental solutions and general solutions of convection–diffusion equation. To demonstrate their efficacy, we applied the high-order general solutions to t...