G. Yuan

Publications119
h-index20
Citations1,145
Highly Influential Citations33
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Monotone finite volume schemes for diffusion equations on polygonal meshes
TLDR
We construct a nonlinear finite volume (FV) scheme for diffusion equation on star-shaped polygonal meshes and prove that the scheme is monotone, i.e., it preserves positivity of analytical solutions for strongly anisotropic and heterogeneous full tensor coefficients. Expand
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The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes
TLDR
We construct a new nonlinear finite volume scheme for diffusion equation on polygonal meshes and prove that the scheme satisfies the discrete extremum principle. Expand
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A Stability Analysis of Hybrid Schemes to Cure Shock Instability
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A Nine Point Scheme for the Approximation of Diffusion Operators on Distorted Quadrilateral Meshes
TLDR
A nine point scheme is presented for discretizing diffusion operators on distorted quadrilateral meshes. Expand
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An improved monotone finite volume scheme for diffusion equation on polygonal meshes
TLDR
We construct a new nonlinear monotone finite volume scheme for diffusion equation on polygonal meshes. Expand
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An efficient explicit/implicit domain decomposition method for convection‐diffusion equations
A nonoverlapping domain decomposition method for some time-dependent convection-diffusion equations is presented. It combines predictor-corrector technique, modified upwind differences with… Expand
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A new nonlinear finite volume scheme preserving positivity for diffusion equations
TLDR
We present a new nonlinear finite volume scheme preserving positivity for diffusion equations. Expand
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Monotone Finite Volume Schemes of Nonequilibrium Radiation Diffusion Equations on Distorted Meshes
TLDR
We construct a monotone finite volume scheme on distorted meshes for multimaterial, nonequilibrium radiation diffusion problems, which are described by the coupled radiation diffusion and material conduction equations. Expand
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Linearity preserving nine-point schemes for diffusion equation on distorted quadrilateral meshes
TLDR
We employ the so-called linearity preserving method, which requires that a difference scheme should be exact on linear solutions, to derive a nine-point difference scheme for the numerical solution of diffusion equation on the structured quadrilateral meshes. Expand
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Alternating group explicit method for the dispersive equation
TLDR
An alternating group explicit method for the numerical solution of a linear dispersive equation with periodic boundary condition . Expand
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