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Steve Shkolle - One of the best experts on this subject based on the ideXlab platform.

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    Journal of Computational Physics, 2019
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    Abstract This is the second part to our companion paper [18] . Herein, we generalize to two space dimensions the C-method developed in [20] , [18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. Solutions to our C-equations not only indicate the location of the shocks and contacts, but also track the geometry of the evolving fronts. This allows us to implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska & Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    arXiv: Computational Physics, 2018
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

Raaghav Ramani - One of the best experts on this subject based on the ideXlab platform.

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    Journal of Computational Physics, 2019
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    Abstract This is the second part to our companion paper [18] . Herein, we generalize to two space dimensions the C-method developed in [20] , [18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. Solutions to our C-equations not only indicate the location of the shocks and contacts, but also track the geometry of the evolving fronts. This allows us to implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska & Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    arXiv: Computational Physics, 2018
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

Jo M Reisne - One of the best experts on this subject based on the ideXlab platform.

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    Journal of Computational Physics, 2019
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    Abstract This is the second part to our companion paper [18] . Herein, we generalize to two space dimensions the C-method developed in [20] , [18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. Solutions to our C-equations not only indicate the location of the shocks and contacts, but also track the geometry of the evolving fronts. This allows us to implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. To test the methodology, we use a highly simplified WENO-based discretization scheme. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska & Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

  • A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: the 2-D case
    2019
    Co-Authors: Ramani Raaghav, Jo M Reisne, Shkolle Steve
    Abstract:

    This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.Comment: 53 pages, 27 figures, to appear in Journal of Computational Physic

  • a space time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme part 2 the 2 d case
    arXiv: Computational Physics, 2018
    Co-Authors: Raaghav Ramani, Jo M Reisne, Steve Shkolle
    Abstract:

    This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.

Jinde Cao - One of the best experts on this subject based on the ideXlab platform.

  • periodic Oscillatory Solution in delayed competitive cooperative neural networks a decomposition approach
    Chaos Solitons & Fractals, 2006
    Co-Authors: Kun Yuan, Jinde Cao
    Abstract:

    In this paper, the problems of exponential convergence and the exponential stability of the periodic Solution for a general class of non-autonomous competitive–cooperative neural networks are analyzed via the decomposition approach. The idea is to divide the connection weights into inhibitory or excitatory types and thereby to embed a competitive–cooperative delayed neural network into an augmented cooperative delay system through a symmetric transformation. Some simple necessary and sufficient conditions are derived to ensure the componentwise exponential convergence and the exponential stability of the periodic Solution of the considered neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice.

  • exponential stability and periodic Oscillatory Solution in bam networks with delays
    IEEE Transactions on Neural Networks, 2002
    Co-Authors: Jinde Cao, Lin Wang
    Abstract:

    Both exponential stability and periodic Oscillatory Solution of bidirectional associative memory (BAM) networks with axonal signal transmission delays are considered by constructing suitable Lyapunov functional and some analysis techniques. Some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic Oscillatory Solutions of BAM with delays. These conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic Oscillatory neural circuits for BAM with delays. In addition, two examples are given to illustrate the results.

  • periodic oscillation and exponential stability of delayed cnns
    Physics Letters A, 2000
    Co-Authors: Jinde Cao
    Abstract:

    Abstract Both the global exponential stability and the periodic oscillation of a class of delayed cellular neural networks (DCNNs) is further studied in this Letter. By applying some new analysis techniques and constructing suitable Lyapunov functionals, some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic Oscillatory Solution of DCNNs. These conditions can be applied to design globally exponentially stable DCNNs and periodic Oscillatory DCNNs and easily checked in practice by simple algebraic methods. These play an important role in the design and applications of DCNNs.

  • periodic Oscillatory Solution of bidirectional associative memory networks with delays
    Physical Review E, 2000
    Co-Authors: Jinde Cao, Lin Wang
    Abstract:

    Periodic Oscillatory phenomena of bidirectional associative memory (BAM) networks with axonal signal transmission delays are investigated by constructing suitable Lyapunov functionals and some analysis techniques. Some simple sufficient conditions are derived ensuring the existence and uniqueness of periodic Oscillatory Solutions of the BAM with delays, and all other Solutions of the BAM converge exponentially to a periodic Oscillatory Solution. These conditions are presented in terms of system parameters, and have an important leading significance in the design and applications of periodic Oscillatory neural circuits for the BAM with delays.

Shkolle Steve - One of the best experts on this subject based on the ideXlab platform.

  • A space-time smooth artificial viscosity method with wavelet noise indicator and shock collision scheme, Part 2: the 2-D case
    2019
    Co-Authors: Ramani Raaghav, Jo M Reisne, Shkolle Steve
    Abstract:

    This is the second part to our companion paper [18]. Herein, we generalize to two space dimensions the C-method developed in [20,18] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities. For gas dynamics, the C-method couples the Euler equations to scalar reaction-diffusion equations, which we call C-equations, whose Solutions serve as space-time smooth artificial viscosity indicators for shocks and contacts. We develop a high-order numerical algorithm for gas dynamics in 2-D which can accurately simulate the Rayleigh-Taylor (RT) instability with Kelvin-Helmholtz (KH) roll-up of the contact discontinuity, as well as shock collision and bounce-back. We implement both directionally isotropic and anisotropic artificial viscosity schemes, the latter adding diffusion only in directions tangential to the evolving front. We additionally produce a novel shock collision indicator function, which naturally activates during shock collision, and then smoothly deactivates. Moreover, we implement a high-frequency 2-D wavelet-based noise detector together with an efficient and localized noise removal algorithm. We provide numerical results for some classical 2-D test problems, including the RT problem, the Noh problem, a circular explosion problem from the Liska and Wendroff [13] review paper, the Sedov blast wave problem, the double Mach 10 reflection test, and a shock-wall collision problem. In particular, we show that our artificial viscosity method can eliminate the wall-heating phenomenon for the Noh problem, and thereby produce an accurate, non-Oscillatory Solution, even though our simplified WENO-type scheme fails to run for this problem.Comment: 53 pages, 27 figures, to appear in Journal of Computational Physic