Adaptive numerical simulation of traffic flow density

Soheili, Ali Reza; Kerayechian, Asghar; Tareghian, Hamed Reza; Davoodi, Nooshin

doi:10.1016/j.camwa.2013.04.025

Cited by 4 publications

(4 citation statements)

References 19 publications

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“…Pengamatan lalu lintas pada pendekatan ini tidak memperhitungkan mobil-mobil secara individu melainkan hanya memperhitungkan kepadatannya saja. Model ini merupakan sistem kesatuan antara: kondisi lalu lintas, kecepatan, dan densitas dalam suatu interval waktu yang membentuk aliran lalu lintas dalam setiap aspek secara keseluruhan [10].…”

Section: A Model Arus Lalu Lintasunclassified

“…Seperti pada Gambar 4 sebelumnya, yaitu mengilustrasikan perubahan nilai n k i pada setiap langkah t k menggunakan persamaan (10). Nilai n i diperbaharui dengan menggunakan fluks dari batas kiri dan kanan.…”

Section: A Skema Numerik Persamaan Kinematik Lwr Menggunakan Metode unclassified

“…Adapun salah satu solusinya, dengan menemukan variasi model matematika yang sesuai dengan permasalahan yang ada di jalan raya. Beberapa ahli matematika telah melakukan penelitian dengan menggunakan banyak pendekatan teori, seperti: teori fundamental kalkulus, hukum konservasi integral, persamaan diferensial parsial, dan alternatif penurunan rumus lainnya untuk mendapatkan model penyelesaian masalah dalam bidang lalu lintas [10]. Contoh dari penelitian yang pernah dilakukan oleh beberapa ahli dapat dilihat pada referensi [1], [3].…”

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Simulasi Berbagai Situasi Traffic Flow Menggunakan Persamaan Kinematik dan Implementasi Metode Finite Volume

Putra

2018

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Jurnal ini membahas mengenai aliran lalu lintas yang dimodelkan dengan persamaan kinematik Lightill, Whitman, dan Richard (LWR). Skema numerik finite volume diterapkan untuk menyelesaikan persamaan tersebut. Skema ini digunakan untuk menyimulasikan dua kondisi penting, yaitu: bertambahnya panjang antrian kendaraan (shock wave), dan terurainya tumpukan kendaraan saat lampu hijau mulai menyala (rarefaction wave). Selanjutnya skema juga digunakan untuk mensimulasikan bertambahnya kepadatan lalu lintas akibat penyempitan ruas jalan, serta akibat penutupan jalan.Kata Kunci:persamaan Kinematic LWR, shock wave, rarefaction wave, metode finite volume

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Section: A Model Arus Lalu Lintasunclassified

Section: A Skema Numerik Persamaan Kinematik Lwr Menggunakan Metode unclassified

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Simulasi Berbagai Situasi Traffic Flow Menggunakan Persamaan Kinematik dan Implementasi Metode Finite Volume

Putra

2018

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“…Microscopic models have many applications, such as trafc forecasting, accident detection, and trafc control, which are typically described using a system of nonlinear partial differential equations. Macroscopic trafc models look at trafc fow as a cumulative concept and are commonly used to analyze service level and also supply and demand, during regional planning or surface transportation networks [12]. In 1955, Lighthill and Whitham and, in 1956, Richards showed that equations expressing water fow could explain the fow of car trafc.…”

Section: Introductionmentioning

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Adaptive Numerical Method for Approximation of Traffic Flow Equations

Najafzadeh

Abbasbandy

Shivanian

2022

Journal of Advanced Transportation

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For a long time now, traffic equations have been considered, and different modeling has been done for it. In this article, we work on the macroscopic model, especially the most famous light model. Because these models are among the stiff and shocking problems, theoretical methods do not give good answers to these problems. This paper describes a meshless method to solve the traffic flow equation as a stiff equation. In the proposed method, we also use the exponential time differencing (ETD) method and the exponential time differencing fourth-order Runge–Kutta (ETDRK4). The purpose of this new method is to use methods of the moving least squares (MLS) method and a modified exponential time differencing fourth-order Runge–Kutta scheme. To solve these equations, we use the meshless method MLS to approximate the spatial derivatives and then use method ETDRK4 to obtain approximate solutions. In order to improve the possible instabilities of method ETDRK4, approaches have been stated. The MLS method provided good results for these equations due to its high flexibility and high accuracy and has a moving window and obtains the solution at the shock point without any false oscillations. The technique is described in detail, and a number of computational examples are presented.

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