A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case

Reyes, Adam; Lee, Dongwook; Graziani, Carlo; Tzeferacos, Petros

doi:10.1007/s10915-017-0625-2

Title: A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case

Authors:

Reyes, Adam;

; Graziani, Carlo; Tzeferacos, Petros

Publication Date:: 2017-12-06

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA)

OSTI Identifier:: 1411478

Grant/Contract Number:: Through the Argonne Institute for Computing in Science under field work proposal 57789; B523820

Resource Type:: Published Article

Journal Name:: Journal of Scientific Computing

Additional Journal Information:: Journal Name: Journal of Scientific Computing Journal Volume: 76 Journal Issue: 1; Journal ID: ISSN 0885-7474

Publisher:: Springer Science + Business Media

Country of Publication:: United States

Language:: English

Citation Formats


                    Reyes, Adam, Lee, Dongwook, Graziani, Carlo, and Tzeferacos, Petros. A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case.  United States: N. p., 2017. 
Web.  doi:10.1007/s10915-017-0625-2.

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                    Reyes, Adam, Lee, Dongwook, Graziani, Carlo, & Tzeferacos, Petros. A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case.  United States.  https://doi.org/10.1007/s10915-017-0625-2

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                    Reyes, Adam, Lee, Dongwook, Graziani, Carlo, and Tzeferacos, Petros. Wed .  
"A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case".  United States.  https://doi.org/10.1007/s10915-017-0625-2.

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@article{osti_1411478,

  title        = {A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case},

  author       = {Reyes, Adam and Lee, Dongwook and Graziani, Carlo and Tzeferacos, Petros},

  abstractNote = {},

  doi          = {10.1007/s10915-017-0625-2},

  journal      = {Journal of Scientific Computing},

  number       = 1,

  volume       = 76,

  place        = {United States},

  year         = {2017},

  month        = {12}

}

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Works referenced in this record:

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Title: A New Class of High-Order Methods for Fluid Dynamics Simulations Using Gaussian Process Modeling: One-Dimensional Case

Citation Formats

Efficient implementation of essentially non-oscillatory shock-capturing schemes, II journal, July 1989

A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics journal, June 2013

Restoration of the contact surface in the HLL-Riemann solver journal, July 1994

A Comparison of Various Meshless Schemes Within a Unified Algorithm conference, June 2012

A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations journal, August 2007

Stable computation of multiquadric interpolants for all values of the shape parameter journal, September 2004

On Postshock Oscillations Due to Shock Capturing Schemes in Unsteady Flows journal, January 1997

Recovery of High Order Accuracy in Radial Basis Function Approximations of Discontinuous Problems journal, March 2010

Riemann Solvers and Numerical Methods for Fluid Dynamics book, January 2009

A RBF-WENO finite volume method for hyperbolic conservation laws with the monotone polynomial interpolation method journal, February 2017

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems journal, February 2009

The behavior of flux difference splitting schemes near slowly moving shock waves journal, September 1990

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD journal, August 2010

Adaptive Tuning of Numerical Weather Prediction Models: Randomized GCV in Three- and Four-Dimensional Data Assimilation journal, November 1995

A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains journal, March 2015

The numerical simulation of two-dimensional fluid flow with strong shocks journal, April 1984

Multiquadric equations of topography and other irregular surfaces journal, March 1971

A high-order finite-volume method for conservation laws on locally refined grids journal, January 2011

Very-high-order weno schemes journal, December 2009

Total-Variation-Diminishing Time Discretizations journal, November 1988

Multiphysics simulations: Challenges and opportunities journal, February 2013

On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes journal, March 2011

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws journal, April 1978

A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains journal, March 2015

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids journal, February 2014

A finite volume method based on radial basis functions for two-dimensional nonlinear diffusion equations journal, October 2006

Uniformly high order accurate essentially non-oscillatory schemes, III journal, August 1987

Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics journal, November 2003

On choosing “optimal” shape parameters for RBF approximation journal, March 2007

Stable computations with flat radial basis functions using vector-valued rational approximations journal, February 2017

A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction–Diffusion Equations on Surfaces journal, September 2014

Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation journal, June 2010

Approximate Riemann solvers, parameter vectors, and difference schemes journal, October 1981

The Effects of Numerical Viscosities journal, July 1996

Trends in supercomputing: The European path to exascale journal, September 2011

Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws journal, January 1996

A numerical study of postshock oscillations in slowly moving shock waves journal, September 2003

Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method journal, July 1979

Finite volume methods for hyperbolic conservation laws journal, April 2007

Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers journal, September 2011

Weighted Essentially Non-oscillatory Schemes journal, November 1994

Computing challenges of the cosmic microwave background journal, January 1999

Gaussian Processes for Machine Learning book, January 2005

The Piecewise Parabolic Method (PPM) for gas-dynamical simulations journal, April 1984

On Godunov-type methods near low densities journal, February 1991

On the Gibbs Phenomenon and Its Resolution journal, January 1997

Computations of Slowly Moving Shocks journal, September 1997

Efficient Implementation of Weighted ENO Schemes journal, June 1996

An HLLC Riemann solver for magneto-hydrodynamics journal, February 2005

An upwind differencing scheme for the equations of ideal magnetohydrodynamics journal, April 1988

Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics journal, April 2003

Stability of Radial Basis Function Methods for Convection Problems on the Circle and Sphere journal, April 2016

Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
journal, July 1989

A solution accurate, efficient and stable unsplit staggered mesh scheme for three dimensional magnetohydrodynamics
journal, June 2013

Restoration of the contact surface in the HLL-Riemann solver
journal, July 1994

A Comparison of Various Meshless Schemes Within a Unified Algorithm
conference, June 2012

A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations
journal, August 2007

Stable computation of multiquadric interpolants for all values of the shape parameter
journal, September 2004

On Postshock Oscillations Due to Shock Capturing Schemes in Unsteady Flows
journal, January 1997

Recovery of High Order Accuracy in Radial Basis Function Approximations of Discontinuous Problems
journal, March 2010

Riemann Solvers and Numerical Methods for Fluid Dynamics
book, January 2009

A RBF-WENO finite volume method for hyperbolic conservation laws with the monotone polynomial interpolation method
journal, February 2017

High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
journal, February 2009

The behavior of flux difference splitting schemes near slowly moving shock waves
journal, September 1990

High-order conservative finite difference GLM–MHD schemes for cell-centered MHD
journal, August 2010

Adaptive Tuning of Numerical Weather Prediction Models: Randomized GCV in Three- and Four-Dimensional Data Assimilation
journal, November 1995

A Kansa-Radial Basis Function Method for Elliptic Boundary Value Problems in Annular Domains
journal, March 2015

The numerical simulation of two-dimensional fluid flow with strong shocks
journal, April 1984

Multiquadric equations of topography and other irregular surfaces
journal, March 1971

A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011

Very-high-order weno schemes
journal, December 2009

Total-Variation-Diminishing Time Discretizations
journal, November 1988

Multiphysics simulations: Challenges and opportunities
journal, February 2013

On the Order of Accuracy and Numerical Performance of Two Classes of Finite Volume WENO Schemes
journal, March 2011

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

A Reduced Radial Basis Function Method for Partial Differential Equations on Irregular Domains
journal, March 2015

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids
journal, February 2014

A finite volume method based on radial basis functions for two-dimensional nonlinear diffusion equations
journal, October 2006

Uniformly high order accurate essentially non-oscillatory schemes, III
journal, August 1987

Non-uniform convergence of finite volume schemes for Riemann problems of ideal magnetohydrodynamics
journal, November 2003

On choosing “optimal” shape parameters for RBF approximation
journal, March 2007

Stable computations with flat radial basis functions using vector-valued rational approximations
journal, February 2017

A Radial Basis Function (RBF)-Finite Difference (FD) Method for Diffusion and Reaction–Diffusion Equations on Surfaces
journal, September 2014

Radial Basis Function Interpolation on Irregular Domain through Conformal Transplantation
journal, June 2010

Approximate Riemann solvers, parameter vectors, and difference schemes
journal, October 1981

The Effects of Numerical Viscosities
journal, July 1996

Trends in supercomputing: The European path to exascale
journal, September 2011

Optimal recovery using thin plate splines in finite volume methods for the numerical solution of hyperbolic conservation laws
journal, January 1996

A numerical study of postshock oscillations in slowly moving shock waves
journal, September 2003

Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method
journal, July 1979

Finite volume methods for hyperbolic conservation laws
journal, April 2007

Matrix Stability of Multiquadric Radial Basis Function Methods for Hyperbolic Equations with Uniform Centers
journal, September 2011

Weighted Essentially Non-oscillatory Schemes
journal, November 1994

Computing challenges of the cosmic microwave background
journal, January 1999

Gaussian Processes for Machine Learning
book, January 2005

The Piecewise Parabolic Method (PPM) for gas-dynamical simulations
journal, April 1984

On Godunov-type methods near low densities
journal, February 1991

On the Gibbs Phenomenon and Its Resolution
journal, January 1997

Computations of Slowly Moving Shocks
journal, September 1997

Efficient Implementation of Weighted ENO Schemes
journal, June 1996

An HLLC Riemann solver for magneto-hydrodynamics
journal, February 2005

An upwind differencing scheme for the equations of ideal magnetohydrodynamics
journal, April 1988

Uniqueness conditions for Riemann problems of ideal magnetohydrodynamics
journal, April 2003

Stability of Radial Basis Function Methods for Convection Problems on the Circle and Sphere
journal, April 2016