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"Persamaan Euler merupakan salah satu penyederhanaan persamaan Navier-Stokes dengan asumsi inviscid, adiabatik serta menghilangkan efek dari body force. Pada aliran kompresibel, persamaan Euler merupakan sistem pesamaan hiperbolik non-linear untuk hukum konservasi. Pada aliran kompresibel, munculnya fenomena diskontinuitas berupa gelombang kejut sering menimbulkan masalah dalam simulasi, terutama dalam hal akurasi. Pada skema Godunov, akurasi interpolasi untuk memperoleh fluks pada batas antar sel dapat ditingkatkan dengan penggunaan limiter. Salah satu limiter orde tinggi yang dapat digunakan dalam penyelesaian persamaan Euler adalah skema weighted essentially non-oscillatory (WENO). Masalah yang timbul dari penggunaan skema WENO sebagai limiter adalah beban komputasi yang sangat tinggi, terlebih jika sistem persamaan dan domain komputasi yang kompleks. Pengurangan beban komputasi dapat dilakukan dengan cara simplifikasi skema WENO itu sendiri atau dengan menggunakan skema hibrid dimana skema WENO akan digunakan pada kondisi tertentu. Pada penelitian ini dikembangkan skema hibrid orde tinggi yang mengadopsi WENO pada daerah diskontinu dengan deteksi diskontinuitas secara lokal. Metode cell-centered finite volume digunakan untuk diskretisasi ruang. Penyelesaian masalah Riemann pada batas sel digunakan skema Harten-Lax-van Leer contact (HLLC) dan Lax-Friedrichs, serta untuk integrasi waktu digunakan skema strong stability preserving Runge-Kutta orde ketiga untuk memberikan kestabilan yang baik pada skema numerik. Berdasarkan hasil yang diperoleh, skema hibrid yang dikembangkan cukup efektif digunakan dalam penyelesaian masalah aliran kompresibel. Pengurangan waktu komputasi yang signifikan dan akurasi yang baik menjadikan skema hibrid yang dikembangkan menjadi salah satu pilihan skema numerik orde tinggi yang baik untuk dapat diterapkan dalam simulasi aliran kompresibel.

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Euler equation is a simplification of Navier-Stokes equation which assume the flows are inviscid, adiabatic, and eliminating the effects of body forces. In the compressible flow, the Euler equation is a non-linear hyperbolic conservation laws. The presence of the discontinuities phenomenon in the form of shock wave in the compressible flow often arise the problem in the simulation, mainly in the terms of accuracy. In the Godunovs scheme, the accuracy of interpolation to obtain flux at the intercell boundary can be improved by using a high order limiter. One of the high order limiter that can be used to solve the Euler equation is weighted essentially non-oscillatory (WENO) scheme.

The problem that arises from the use of WENO scheme is high computational loads, moreover the system of equations or the domain are very complex. To reduce the computational cost, it can be done by simplify the WENO reconstruction or implement the hybrid scheme where the WENO scheme only applied in certain conditions.

In this study, hybrid high order scheme are developed which adopt the WENO schem in the discontinuous region by detecting the local discontinuities. The cell-centered finite volume are used in the spatial discretization. Harten-Lax-van Leer contact (HLLC) and Lax-Friedrichs scheme are used to solve Riemann problem in the cell boundary, and third order strong stability preserving Runge-Kutta (SSP-RK) scheme is used for time integration to ensure the positivity and provide good stability in the numerical scheme.

The results shows that the hybrid scheme developed in this work are effective for solving compressible flow problem. The significant reduction of the computational cost and the satisfactory accuracy results are make this hibrid scheme become one of the good choices of high order numerical scheme to be applied in the compressible flow simulation."

"This book is intended as a text for undergraduate and graduate courses in aerodynamics, typically offered to students of aerospace and mechanical engineering programs. It covers all aspects of aerodynamics. The book begins with a description of the standard atmosphere and basic concepts, then moves on to cover the equations and mathematical models used to describe and characterize flow fields, as well as their thermodynamic aspects and applications. Specific emphasis is placed on the relation between concepts and their use in aircraft design. Additional topics of interest to the reader are presented in the Appendix, which draws on the teachings provided in the text. The book is written in an easy to understand manner, with pedagogical aids such as chapter overviews, summaries, and descriptive and objective questions to help students evaluate their progress. Atmospheric and gas tables are provided to facilitate problem solving. Lastly, a detailed bibliography is included at the end of each chapter to provide students with further resources. The book can also be used as a text for professional development courses in aerodynamics."

"This book provides an elementary introduction to some one-dimensional fluid flow problems involving shock waves in air. The differential equations of fluid flow are approximated by finite difference equations and these in turn are numerically integrated in a stepwise manner. Artificial viscosity is introduced into the numerical calculations in order to deal with shocks. The presentation is restricted to the finite-difference approach to solve the coupled differential equations of fluid flow as distinct from finite-volume or finite-element methods. This text presents the results arising from the numerical solution using Mathcad programming. Both plane and spherical shock waves are discussed with particular emphasis on very strong explosive shocks in air. "