Robust and efficient finite-difference-time-domain modelling of the propagation of nonlinear elastic waves

• Autorzy: Pandala A. , Shivaprasad S. , Krishnamurthy C. V. , Balasubramaniam K.

Identyfikatory

DOI

10.26357/BNiD.2018.008

Warianty tytułu

PL

Niezawodne i wydajne modelowanie propagacji nieliniowych fal sprężystych metodą różnic skończonych w dziedzinie czasu

• Języki publikacji: EN

Abstrakty

EN

A robust finite-difference-time-domain (FDTD ) scheme to model the non-linear elastic wave propagation in a homogeneous isotropic material is presented. A formulation based on rotated staggered grid scheme in a displacement-velocity-stress configuration incorporating both geometric and material nonlinearities is proposed. By adopting a Parsimonious algorithm, the computational memory requirement is reduced by 50%. Simulations are accelerated by exploiting massive data parallelism innate to the FDTD approach using parallel computation on Graphical Processing Units with NVIDIA CUDA ’s API. For the proposed numerical scheme, the grid convergence criterion and accuracy over propagating distances are investigated. The study is also extended to determine the contribution from geometric and material models at various input amplitude levels. The time and frequency domain signals obtained from the proposed scheme are verified with a commercial finite element solver. The simulation runtimes for an Aluminium sample of dimensions 20 mm x 10 mm using a 5 MHz pulse is of the order of one minute, which makes the proposed numerical scheme attractive to model nonlinear elastic waves in large domains.

PL

W artykule przedstawiono odporny schemat metody różnic skończonych w dziedzinie czasu (FDTD ) do modelowania propagacji nieliniowych fal sprężystych w jednorodnym materiale izotropowym. Zaproponowano podejście oparte na rotowanych siatkach przestawnych w układzie przemieszczenie- prędkość-naprężenie obejmującym zarówno nieliniowość geometryczną, jak i materiałową. Zastosowanie algorytmu redukcji oszczędnej, zmniejszyło zapotrzebowanie na pamięć obliczeniową o 50%. Symulacje są przyspieszane przez wykorzystanie olbrzymiego paralelizmu danych wbudowanego w podejście FDTD z wykorzystaniem obliczeń równoległych na jednostkach przetwarzania graficznego (GPU) wyposażonych w interfejs API NVIDIA CUDA . Dla proponowanego schematu numerycznego badane jest kryterium zbieżności siatki i dokładność w funkcji odległości propagacji. Badanie rozszerzono również w celu określenia wkładu modeli geometrycznych i materiałowych na różnych poziomach amplitudy wejściowej. Sygnały w dziedzinie czasu i częstotliwości uzyskane z proponowanego schematu są weryfikowane za pomocą komercyjnego oprogramowania wykorzystującego metodę elementów skończonych. Czasy pracy dla symulacji propagacji impulsu o częstotliwości 5 MHz w próbce aluminium o wymiarach 20 mm x 10 mm są rzędu jednej minuty, co sprawia, że proponowany schemat liczbowy jest atrakcyjny dla modelowania nieliniowych fal sprężystych w dużych domenach.

Słowa kluczowe

EN

Finite Difference Time Domain; Rotated Staggered Grid; Parsimonious Scheme; Nonlinear elastic waves; CUDA; GPU

PL

metoda różnic skończonych w dziedzinie czasu; rotowane siatki przestawne; schemat redukcji oszczędnej; nieliniowe fale sprężyste; CUDA; GPU

• Wydawca: Stowarzyszenie Inżynierów i Techników Mechaników Polskich
• Czasopismo: Badania Nieniszczące i Diagnostyka
• Rocznik: 2018
• Tom: nr 2
• Strony: 11--21
• Opis fizyczny: Bibliogr. 56 poz., rys., tab.

Twórcy

autor

Pandala A.

• Centre for Non-Destructive Evaluation, Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai, India

autor

Shivaprasad S.

• Centre for Non-Destructive Evaluation, Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai, India

autor

Krishnamurthy C. V.

• Centre for Non-Destructive Evaluation, Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai, India
• Department of Physics, Indian Institute of Technology, Madras, Chennai, India

autor

Balasubramaniam K.

• Centre for Non-Destructive Evaluation, Department of Mechanical Engineering, Indian Institute of Technology, Madras, Chennai, India

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).