Non-diffusive neural network method for hyperbolic conservation laws

Fuente: arXiv
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Main Authors: Lorin, Emmanuel, Novruzi, Arian
Format: Preprint
Published: 2024
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_version_ 1866916259339173888
author Lorin, Emmanuel
Novruzi, Arian
author_facet Lorin, Emmanuel
Novruzi, Arian
contents In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.
format Preprint
id arxiv_https___arxiv_org_abs_2405_15559
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Non-diffusive neural network method for hyperbolic conservation laws
Lorin, Emmanuel
Novruzi, Arian
Numerical Analysis
35A35, 35L02, 35L65, 35D30, 65M55
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.
title Non-diffusive neural network method for hyperbolic conservation laws
topic Numerical Analysis
35A35, 35L02, 35L65, 35D30, 65M55
url https://arxiv.org/abs/2405.15559