Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation

Journal Article · 01 January 2022 · Communications in Computational Physics

DOI: https://doi.org/10.4208/cicp.oa-2021-0063 · OSTI ID:2282984

Cai, Min ^[1]; Kharazmi, Ehsan ^[2]; Li, Changpin ^[3]; Karniadakis, George Em ^[4]

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1. Shanghai University (China); Brown University
2. Brown University, Providence, RI (United States)
3. Shanghai University (China)
4. Brown University, Providence, RI (United States); Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

We develop fractional buffer layers (FBLs) to absorb propagating waves without reflection in bounded domains. Our formulation is based on variable-order spatial fractional derivatives. We select a proper variable-order function so that dissipation is induced to absorb the coming waves in the buffer layers attached to the domain. In particular, we first design proper FBLs for the one-dimensional one-way and two-way wave propagation. Then, we extend our formulation to two-dimensional problems, where we introduce a consistent variable-order fractional wave equation. In each case, we obtain the fully discretized equations by employing a spectral collocation method in space and Crank-Nicolson or Adams-Bashforth method in time. We compare our results with a finely tuned perfectly matched layer (PML) method and show that the proposed FBL is able to suppress reflected waves including corner reflections in a two-dimensional rectangular domain. Here, we also demonstrate that our formulation is more robust and uses less number of equations.

• Research Organization: Brown University, Providence, RI (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0019453
• OSTI ID: 2282984
• Journal Information: Communications in Computational Physics, Journal Name: Communications in Computational Physics Journal Issue: 2 Vol. 31; ISSN 1815-2406
• Publisher: Global Science PressCopyright Statement
• Country of Publication: United States
• Language: English