Xiaodong Liu

Works (8)

Updated: July 5th, 2023 15:39

2022 article

A reconstructed discontinuous Galerkin method based on variational formulation for compressible flows

Li, L., Liu, X., & Luo, H. (2022, July 3). Journal of Computational Physics.

By: L. Li n, X. Liu* & H. Luo n

author keywords: ReconstructeddiscontinuousGalerkin; Variationalreconstruction; High-order; Compactreconstruction; Interfacialjumpintegration
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics; Lattice Boltzmann Simulation Studies
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Source: Web Of Science
Added: August 1, 2022

2019 article

Reconstructed Discontinuous Galerkin Methods for Hyperbolic Diffusion Equations on Unstructured Grids

Lou, J., Liu, X., Luo, H., & Nishikawa, H. (2019, January 31). Communications in Computational Physics.

By: J. Lou, X. Liu*, H. Luo* & H. Nishikawa

author keywords: Discontinuous Galerkin methods; first-order hyperbolic system; unstructured grids
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Computational Fluid Dynamics and Aerodynamics; Advanced Mathematical Modeling in Engineering
TL;DR: Numerical experiments demonstrate that the developed hyperbolic rDG methods are able to achieve the designed optimal order of accuracy for both solutions and their derivatives on regular, irregular, and heterogeneous girds, and outperform the BR2 method in terms of the magnitude of the error. (via Semantic Scholar)
Source: Web Of Science
Added: February 4, 2019

2017 article

A Parallel, High-Order Direct Discontinuous Galerkin Method for the Navier-Stokes Equations on 3D Hybrid Grids

Cheng, J., Liu, X., Liu, T., & Luo, H. (2017, March 27). Communications in Computational Physics.

By: J. Cheng *, X. Liu n, T. Liu * & H. Luo n

author keywords: Direct discontinuous Galerkin method; compressible Navier-Stokes equations; hybrid grids
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics; Model Reduction and Neural Networks
TL;DR: The numerical results obtained indicate that theDDG method can achieve the designed order of accuracy and is able to deliver comparable results as the widely used BR2 scheme, clearly demonstrating that the DDG method provides an attractive alternative for solving the 3D compressible Navier-Stokes equations. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2017 article

A reconstructed discontinuous Galerkin method for compressible turbulent flows on 3D curved grids

Liu, X., Xia, Y., & Luo, H. (2017, October 23). Computers & Fluids.

By: X. Liu n, Y. Xia * & H. Luo n

author keywords: Discontinuous Galerkin; WEND; RANS; Curved elements
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics; Lattice Boltzmann Simulation Studies
TL;DR: A third-order accurate reconstructed discontinuous Galerkin method, namely rDG(P1P2), is presented to solve the Reynolds-Averaged Navier–Stokes (RANS) equations, along with the modified one-equation model of Spalart and Allmaras on 3D curved grids. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2017 article

A reconstructed discontinuous Galerkin method for the compressible Navier-Stokes equations on three-dimensional hybrid grids

Liu, X., Xuan, L., Xia, Y., & Luo, H. (2017, May 2). Computers & Fluids.

By: X. Liu n, L. Xuan n, Y. Xia * & H. Luo n

author keywords: Discontinuous Galerkin method; WENO reconstruction; Unstructured grids; Compressible Navier-Stokes equation
topics (OpenAlex): Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics; Fluid Dynamics and Turbulent Flows
TL;DR: The numerical results demonstrate that the rDG(P 1 P 2 ) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the direct numerical simulation (DNS) of compressible turbulent flows. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2016 article

A Comparative Study of Rosenbrock-Type and Implicit Runge-Kutta Time Integration for Discontinuous Galerkin Method for Unsteady 3D Compressible Navier-Stokes equations

Liu, X., Xia, Y., Luo, H., & Xuan, L. (2016, October 1). Communications in Computational Physics.

By: X. Liu n, Y. Xia *, H. Luo n & L. Xuan n

author keywords: Implicit time integration; Rosenbrock-Wanner; discontinuous Galerkin; WENO; Navier-Stokes
topics (OpenAlex): Numerical methods for differential equations; Computational Fluid Dynamics and Aerodynamics; Advanced Numerical Methods in Computational Mathematics
TL;DR: Numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2016 article

A direct discontinuous Galerkin method for the compressible Navier–Stokes equations on arbitrary grids

Cheng, J., Yang, X., Liu, X., Liu, T., & Luo, H. (2016, September 24). Journal of Computational Physics.

By: J. Cheng *, X. Yang, X. Liu n, T. Liu * & H. Luo n

author keywords: Direct discontinuous Galerkin method; Compressible Navier-Stokes equations; Arbitrary grids
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Computational Fluid Dynamics and Aerodynamics; Lattice Boltzmann Simulation Studies
TL;DR: A Direct Discontinuous Galerkin (DDG) method for solving the compressible NavierStokes equations on arbitrary grids is developed and is able to deliver the same accuracy as the widely used BR2 method at a significantly reduced cost. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2015 article

A third‐order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time‐accurate solution of the compressible Navier–Stokes equations

Xia, Y., Liu, X., Luo, H., & Nourgaliev, R. (2015, June 1). International Journal for Numerical Methods in Fluids.

By: Y. Xia *, X. Liu n, H. Luo n & R. Nourgaliev *

author keywords: discontinuous Galerkin; WENO; compressible Navier-Stokes; unsteady flows; implicit Runge-Kutta
topics (OpenAlex): Advanced Numerical Methods in Computational Mathematics; Computational Fluid Dynamics and Aerodynamics; Numerical methods for differential equations
Source: Web Of Science
Added: August 6, 2018

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