Comparison of an explicit-implicit Scheme and a Nonuniform Finite Difference Framework of Two-Dimensional Wave Propagation

Comparison of an explicit-implicit Scheme and a Nonuniform Finite Difference Framework of Two-Dimensional Wave Propagation | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Method Article Comparison of an explicit-implicit Scheme and a Nonuniform Finite Difference Framework of Two-Dimensional Wave Propagation Ujjal Mandal This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9533386/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper gives a nonuniform formulation of the finite difference of the numerical simulation of the wave propagation in 2D. The proposed method, as opposed to classical methods that use uniform grids, uses asymmetric forward and backward spatial discretization to accurately approximate second-order derivative on nonuniform meshes. This representation allows grid-design flexibility, allowing local refinement in areas of interest, but with computational efficiency. Explicit and implicit time integration schemes are used both of which give the explicit scheme computational simplicity and the implicit scheme greater stability with use of matrix-based solution schemes. The resultant discrete system takes the form of a sparse matrix, which can be computed efficiently numerically. A set of numerical experiments is conducted in order to prove the proposed approach. Different grid structures are taken into account such as uniform, non uniform, structured and unstructured grid in order to measure their effects in terms of numerical accuracy and wave propagation characteristics. A grid convergence test confirms that the method has about second-order accuracy. Further verification of the scheme stability and physical consistency is achieved by further analysis of sensor signals, frequency spectra and energy conservation. The presented nonuniform finite difference framework is a powerful, high- fidelity computationally efficient method of simulating wave propagation in complicated domains. Its capability of dealing with nonuniform grids and heterogeneous media renders it applicable in a large number of applications in computational physics and engineering. Computational Mathematics Nonuniform finite difference Wave propagation Finite difference time-domain (FDTD) Nonuniform grid Sparse matrix Implicit and explicit schemes Grid convergence Heterogeneous media Numerical simulation Laplacian discretization Full Text Additional Declarations The authors declare potential competing interests as follows: This manuscript is our original work and has not been published previously, nor is it under consideration for publication elsewhere. The authors declare that there is no conflict of interest regarding the publication of this paper. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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