Enhanced fifth order WENO shock-capturing schemes with deep learning
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Publication:2063299
DOI10.1016/j.rinam.2021.100201zbMath1481.65136arXiv2103.04988OpenAlexW3208889299MaRDI QIDQ2063299
Publication date: 11 January 2022
Published in: Results in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2103.04988
neural networkshyperbolic conservation lawssmoothness indicatorsweighted essentially non-oscillatory methoddeep learning
Artificial neural networks and deep learning (68T07) KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite difference methods for boundary value problems involving PDEs (65N06) Euler equations (35Q31)
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Uses Software
Cites Work
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- Modified non-linear weights for fifth-order weighted essentially non-oscillatory schemes
- Accuracy of the weighted essentially non-oscillatory conservative finite difference schemes
- High order weighted essentially non-oscillatory WENO-Z schemes for hyperbolic conservation laws
- Dispersion-relation-preserving finite differene schemes for computational acoustics
- Controlling oscillations in high-order discontinuous Galerkin schemes using artificial viscosity tuned by neural networks
- Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method. II: Two dimensional case
- High resolution schemes for hyperbolic conservation laws
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- Approximate Riemann solvers, parameter vectors, and difference schemes
- A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
- Hermite WENO schemes and their application as limiters for Runge-Kutta discontinuous Galerkin method: One-dimensional case.
- Hybrid tuned center-difference-WENO method for large eddy simulations in the presence of strong shocks.
- Conservative hybrid compact-WENO schemes for shock-turbulence interaction
- Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers
- A modified fifth-order WENO scheme for hyperbolic conservation laws
- Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
- Efficient implementation of weighted ENO schemes
- DGM: a deep learning algorithm for solving partial differential equations
- A neural network based shock detection and localization approach for discontinuous Galerkin methods
- A reduced-dissipation WENO scheme with automatic dissipation adjustment
- A characteristic-featured shock wave indicator for conservation laws based on training an artificial neuron
- Detecting troubled-cells on two-dimensional unstructured grids using a neural network
- An improved weighted essentially non-oscillatory scheme with a new smoothness indicator
- A new class of adaptive high-order targeted ENO schemes for hyperbolic conservation laws
- A family of high-order targeted ENO schemes for compressible-fluid simulations
- An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws
- Analysis of WENO Schemes for Full and Global Accuracy
- Linear Instability of the Fifth-Order WENO Method
- High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
- Monotone Difference Approximations for Scalar Conservation Laws
- Finite Volume Methods for Hyperbolic Problems
- A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws
- Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning
- A Hermite WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems
- Learning data-driven discretizations for partial differential equations
- Weak solutions of nonlinear hyperbolic equations and their numerical computation
- A Hybrid WENO Method with Modified Ghost Fluid Method for Compressible Two-Medium Flow Problems
- Optimized weighted essentially nonoscillatory schemes for linear waves with discontinuity
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