Partial Fourier Transform Methods to Solve the Solution Formula of Stokes Equation in Half-Space

Authors

  • Sri Maryani Jenderal Soedirman University http://orcid.org/0000-0003-4868-5443
  • Siti Fauziah Zahratunnisa Jenderal Soedirman University
  • Idha Sihwaningrum Jenderal Soedirman University
  • Ari Wardayani Jenderal Soedirman University
  • Bambang Hendriya Guswanto Jenderal Soedirman University

DOI:

https://doi.org/10.23887/jstundiksha.v11i1.39523

Keywords:

Stokes equation, Partial Fourier transform, half space, resolvent problem, Laplace transform

Abstract

Fluida adalah suatu bentuk materi yang memiliki zat cair, gas, dan plasma. Dalam kehidupan sehari-hari, cairan menjadi bagian penting, seperti bagian dari darah dan juga membantu tubuh mendapatkan nutrisi. Selain itu, beberapa fenomena lingkungan terkait erat dengan mekanika fluida. Konsep fluida membantu kita memahami perilaku fluida dengan berbagai kondisi. Telah diketahui bahwa gerak fluida dapat digambarkan dalam model matematika khususnya dalam bentuk persamaan diferensial parsial (PDE) dan disebut sebagai persamaan navier stokes (NSE). Persamaan navier stokes diturunkan dari keseimbangan kekekalan massa dan kekekalan momentum. Dalam penelitian ini mempertimbangkan rumus solusi linierisasi persamaan navier stokes (NSE) dengan masalah nilai batas awal (IBV) dalam ruang setengah tanpa tegangan permukaan. Masalah model yang dipertimbangkan meliputi jenis fluida nonlinier. Prosedur penelitian yang merupakan transformasi model masalah menggunakan transformasi fourier dari sistem persamaan yang baru. Kemudian dihitung rumus solusi dari sistem persamaan baru untuk kecepatan dan kepadatan dari masalah model dengan menggunakan metode transformasi Fourier dan transformasi fourier parsial. Strategi untuk mendapatkan solusi masalah model didasarkan pada analisis beberapa penyelesaian masalah model yang diperoleh dengan menggunakan transformasi laplace dari persamaan stokes. Oleh karena itu, secara khusus, rumus kecepatan v=(v_1,…,v_N ) dan kepadatan (x,t) dari persamaan stokes diperoleh.

Author Biographies

Sri Maryani, Jenderal Soedirman University

Mathematics Department

Siti Fauziah Zahratunnisa, Jenderal Soedirman University

Mathematics Department

Idha Sihwaningrum, Jenderal Soedirman University

Mathematics Department

Ari Wardayani, Jenderal Soedirman University

Mathematics Department

Bambang Hendriya Guswanto, Jenderal Soedirman University

Mathematics Department

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Published

2022-02-27

How to Cite

Maryani, S., Zahratunnisa, S. F., Sihwaningrum, I., Wardayani, A., & Guswanto, B. H. (2022). Partial Fourier Transform Methods to Solve the Solution Formula of Stokes Equation in Half-Space. JST (Jurnal Sains Dan Teknologi), 11(1), 157–164. https://doi.org/10.23887/jstundiksha.v11i1.39523

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