6 Result(s)
within
Jian-Guo Liu
Mathematics
Computational Mathematics and Numerical Analysis
Theoretical, Mathematical and Computational Physics
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Article
On the Dynamics of the Boundary Vorticity for Incompressible Viscous Flows
The dynamical equation of the boundary vorticity has been obtained, which shows that the viscosity at a solid wall is doubled as if the fluid became more viscous at the boundary. For certain viscous flows the ...
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Article
Explicit and Implicit TVD Schemes for Conservation Laws with Caputo Derivatives
In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order and the second order explicit ...
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Article
Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis
In this paper, we apply a simple finite element numerical scheme, proposed in an earlier work (Liu in Math Comput 70(234):579–593, 2000), to perform a high resolution numerical simulation of incompressible flow o...
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Article
A Local Pressure Boundary Condition Spectral Collocation Scheme for the Three-Dimensional Navier–Stokes Equations
A spectral collocation scheme for the three-dimensional incompressible \(({\varvec{u}},p)\) ...
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Article
Concepts and Application of Time-Limiters to High Resolution Schemes
A new class of implicit high-order non-oscillatory time integration schemes is introduced in a method-of-lines framework. These schemes can be used in conjunction with an appropriate spatial discretization sch...
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Article
A Fourth Order Scheme for Incompressible Boussinesq Equations
A fourth order finite difference method is presented for the 2D unsteady viscous incompressible Boussinesq equations in vorticity-stream function formulation. The method is especially suitable for moderate to ...
