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Volume 14, Issue 1
A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws

Uttam Singh Rajput & Krishna Mohan Singh

Adv. Appl. Math. Mech., 14 (2022), pp. 275-298.

Published online: 2021-11

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  • Abstract

In this work, we have developed a fifth-order alternative mapped weighted essentially nonoscillatory (AWENO-M) finite volume scheme using non-linear weights of mapped WENO reconstruction scheme of Henrick et al. (J. Comput. Phys., 207 (2005), pp. 542--567) for solving hyperbolic conservation laws. The reconstruction of numerical flux is done using primitive variables instead of conservative variables. The present scheme results in less spurious oscillations near discontinuities and shows higher-order accuracy at critical points compared to the alternative WENO scheme (AWENO) based on traditional non-linear weights of Jiang and Shu (J. Comput. Phys., 228 (1996), pp. 202--228). The third-order Runge-Kutta method has been used for solution advancement in time. The Harten-Lax-van Leer-Contact (HLLC) shock-capturing method is used to provide necessary upwinding into the solution. The performance of the present scheme is evaluated in terms of accuracy, computational cost, and resolution of discontinuities by using various one and two-dimensional test cases.

  • Keywords

High resolution scheme, unsteady, non-linear weights, numerical fluxes, alternative WENO scheme, hyperbolic equations.

  • AMS Subject Headings

35L65, 65M08

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-275, author = {Uttam Singh and Rajput and and 21443 and and Uttam Singh Rajput and Krishna Mohan and Singh and and 21444 and and Krishna Mohan Singh}, title = {A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2021}, volume = {14}, number = {1}, pages = {275--298}, abstract = {

In this work, we have developed a fifth-order alternative mapped weighted essentially nonoscillatory (AWENO-M) finite volume scheme using non-linear weights of mapped WENO reconstruction scheme of Henrick et al. (J. Comput. Phys., 207 (2005), pp. 542--567) for solving hyperbolic conservation laws. The reconstruction of numerical flux is done using primitive variables instead of conservative variables. The present scheme results in less spurious oscillations near discontinuities and shows higher-order accuracy at critical points compared to the alternative WENO scheme (AWENO) based on traditional non-linear weights of Jiang and Shu (J. Comput. Phys., 228 (1996), pp. 202--228). The third-order Runge-Kutta method has been used for solution advancement in time. The Harten-Lax-van Leer-Contact (HLLC) shock-capturing method is used to provide necessary upwinding into the solution. The performance of the present scheme is evaluated in terms of accuracy, computational cost, and resolution of discontinuities by using various one and two-dimensional test cases.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0320}, url = {http://global-sci.org/intro/article_detail/aamm/19985.html} }
TY - JOUR T1 - A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws AU - Rajput , Uttam Singh AU - Singh , Krishna Mohan JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 275 EP - 298 PY - 2021 DA - 2021/11 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0320 UR - https://global-sci.org/intro/article_detail/aamm/19985.html KW - High resolution scheme, unsteady, non-linear weights, numerical fluxes, alternative WENO scheme, hyperbolic equations. AB -

In this work, we have developed a fifth-order alternative mapped weighted essentially nonoscillatory (AWENO-M) finite volume scheme using non-linear weights of mapped WENO reconstruction scheme of Henrick et al. (J. Comput. Phys., 207 (2005), pp. 542--567) for solving hyperbolic conservation laws. The reconstruction of numerical flux is done using primitive variables instead of conservative variables. The present scheme results in less spurious oscillations near discontinuities and shows higher-order accuracy at critical points compared to the alternative WENO scheme (AWENO) based on traditional non-linear weights of Jiang and Shu (J. Comput. Phys., 228 (1996), pp. 202--228). The third-order Runge-Kutta method has been used for solution advancement in time. The Harten-Lax-van Leer-Contact (HLLC) shock-capturing method is used to provide necessary upwinding into the solution. The performance of the present scheme is evaluated in terms of accuracy, computational cost, and resolution of discontinuities by using various one and two-dimensional test cases.

Uttam Singh Rajput & Krishna Mohan Singh. (1970). A Fifth Order Alternative Mapped WENO Scheme for Nonlinear Hyperbolic Conservation Laws. Advances in Applied Mathematics and Mechanics. 14 (1). 275-298. doi:10.4208/aamm.OA-2020-0320
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