A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws

Christlieb, Andrew; Guo, Wei; Jiang, Yan; Yang, Hyoseon

doi:10.1016/j.jcp.2018.12.011

Cited by 5 publications

(5 citation statements)

References 36 publications

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“…This sample test is usually employed to verify nonoscillatory type and shock-capturing schemes to evaluate their non-oscillatory property and numerical dissipation (Deng et al, 2019;Zhang et al, 2021). This test case was also considered in previous studies by Su and Kim (2018), Huang and Chen (2018), and Liu et al (2018), Christlieb et al, (2019), Deng et al, (2019), and Ha and Lee (2020). However, they generally considered the problem for short-term simulations, i.e., T ≤ 1000 periods.…”

Section: Numerical Test 41 Test 1 Advection Complex Profilesmentioning

confidence: 99%

“…In the present work, the study focuses on evaluating the performance of the TVD filter on several finite difference schemes in simulations starting from short periods T = 2 and 10, medium periods t = 100, to long periods t = 1000, 2000 5000. We use a periodic boundary condition (Christlieb et al, 2019). The calculation is performed using N = 400 cells with C r = U o Δt/Δx = 0.4.…”

Section: Numerical Test 41 Test 1 Advection Complex Profilesmentioning

confidence: 99%

“…The initial condition is φ(x, 0) = 1 and the boundary condition is periodic. The exact solution is (Christlieb et al, 2019) Figure 6. Simulation results of equation ( 9) using RK4MF2, RK6MF2 and FLMF2 with Δ= 2π/400 at t = 5.…”

Section: Test 2 (One Dimensional Equation With Variable Coefficient)mentioning

confidence: 99%

“…This fluid flow field can be viewed as the rotation of a solid body about its center point at the position (0.5,0.5). This case was also studied by Christlieb et al (2019) and Zhang et al (2021), The three solid bodies consist of a slotted cylinder, a cone, and a sinusoidal hump. For given (x o ,y o ) let…”

Section: Test 6: Two-dimensional Pure Convection In Rotating Fluidmentioning

confidence: 99%

“…(ENO) types of schemes (Su and Kim, 2018;Ha,et al, 2019), weighted essentially non-oscillatory (WENO) schemes (Liu and Qiu, 2016;Christlieb et al,2019;Rajput and Singh, 2022), a series of hybrid WENO/central difference methods (Kim and Kwon, 2005), Limiter numerical fluxes schemes using the normalized variable formulation (Leonard, 1988;Leonard and Mohktari, 1990;Gao et al, 2012;Zhang et al, 2021), the Godunov-type schemes with artificial viscosity (Rodionov, 2017) and so on. The methods attempt to capture the discontinuity, generally known as the shock capture schemes.…”

Section: Introductionmentioning

confidence: 99%

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Higher-Order Finite Difference Scheme With TVD Filter Algorithm. Part 1: Simulations of Scalar Advective Dominant Problems.

Cahyono

2022

JTS ITB

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Engquist et al. (1989) proposed non-linear TVD filters. When combined with a traditional higher-order finite difference scheme, these filters can simulate shock or high concentration gradient problems with no spurious oscillations. Among the filter proposed is the filter algorithm 2.2. However, this algorithm flattens extrema that are not the results of overshooting and consequency the scheme reduces to a low order of accuracy locally around smooth extrema. Modification of the TVD filter algorithm 2.2 has been proposed in this paper to overcome this problem. Several conservative finite difference schemes are considered for testing the TVD filter. Non-conservative schemes consisting of 4th and 6th -order Runge-Kutta method are also evaluated. The modified filter has been tested to simulate seven test cases, including a pure advection of scalar profiles, a pure advection with variable velocity, two inviscid burger equations, an advection-diffusion equation with variable velocity and dispersion, advection of three solid bodies in rotating fluid around a square of a side length of 2, and a two-dimensional advection-diffusion equation. The numerical experiments showed that applying the modified TVD filter, combined with the higher-order non-TVD finite difference schemes for solving the advection equation, can produce accurate solutions with no oscillations and no clipping effect extrema. Keywords : Non-Oscillatory schemes, TVD filter, advection, higher-order accurate Abstrak Engquist dkk. (1989) mengusulkan filter TVD non-linear. Ketika dikombinasikan dengan skema beda hingga orde tinggi tradisional, filter ini dapat mensimulasikan kejutan atau masalah gradien konsentrasi tinggi tanpa osilasi palsu. Di antara filter yang diusulkan adalah algoritma filter 2.2. Namun, algoritma ini meratakan ekstrem yang bukan merupakan hasil dari “overshooting” dan konsekuensinya skema tersebut direduksi ke tingkat akurasi yang rendah secara lokal di sekitar ekstrem halus. Modifikasi algoritma filter TVD 2.2 telah diusulkan dalam makalah ini untuk mengatasi masalah ini. Beberapa skema konservatif dipertimbangkan untuk menguji filter TVD. Skema non-konservatif metode Runge-Kutta orde ke-4 dan ke-6 juga dievaluasi. Filter yang dimodifikasi diuji untuk mensimulasikan tujuh kasus, termasuk adveksi murni profil skalar, adveksi murni dengan kecepatan bervariasi, dua persamaan burger inviscid, persamaan adveksi-difusi dengan kecepatan bervariasi dan dispersi, adveksi tiga benda padat berputar oleh aliran di bidang persegi dengan panjang sisi 2, dan persamaan adveksi-difusi dua dimensi. Eksperimen numerik menunjukkan bahwa penerapan filter TVD yang dimodifikasi, dikombinasikan dengan skema beda hingga non-TVD orde tinggi untuk menyelesaikan persamaan adveksi, dapat menghasilkan solusi yang akurat tanpa osilasi dan tanpa efek kliping Kata Kunci : skema tanpa osilasi, Filter TVD, advection, orde-akurasi tinggi

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Section: Numerical Test 41 Test 1 Advection Complex Profilesmentioning

confidence: 99%

Section: Numerical Test 41 Test 1 Advection Complex Profilesmentioning

confidence: 99%

Section: Test 2 (One Dimensional Equation With Variable Coefficient)mentioning

confidence: 99%

Section: Test 6: Two-dimensional Pure Convection In Rotating Fluidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Higher-Order Finite Difference Scheme With TVD Filter Algorithm. Part 1: Simulations of Scalar Advective Dominant Problems.

Cahyono

2022

JTS ITB

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Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave

Wang

2022

Appl. Math. Mech.-Engl. Ed.

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High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation

Christlieb

Link

Yang

et al. 2021

Commun. Appl. Math. Comput.

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A moving mesh WENO method based on exponential polynomials for one-dimensional conservation laws

Cited by 5 publications

References 36 publications

Higher-Order Finite Difference Scheme With TVD Filter Algorithm. Part 1: Simulations of Scalar Advective Dominant Problems.

Higher-Order Finite Difference Scheme With TVD Filter Algorithm. Part 1: Simulations of Scalar Advective Dominant Problems.

Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave

High-Order Semi-Lagrangian WENO Schemes Based on Non-polynomial Space for the Vlasov Equation

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