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Volume 22, Issue 3
A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws

Yaguang Gu & Guanghui Hu

DOI: 10.4208/cicp.OA-2016-0088

Commun. Comput. Phys., 22 (2017), pp. 829-851.

Published online: 2017-09

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  • Abstract

We introduce a third order adaptive mesh method to arbitrary high order Godunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistribution algorithm and solution algorithm. The mesh-redistribution algorithm is derived based on variational approach, while a new solution algorithm is developed to preserve high order numerical accuracy well. The feature of proposed Adaptive ADER scheme includes that 1). all simulations in this paper are stable for large CFL number, 2). third order convergence of the numerical solutions is successfully observed with adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions are obtained successfully when there are shocks in the solution. A variety of numerical examples show the feature well.

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@Article{CiCP-22-829, author = {Yaguang Gu and Guanghui Hu}, title = {A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws}, journal = {Communications in Computational Physics}, year = {2017}, volume = {22}, number = {3}, pages = {829--851}, abstract = {

We introduce a third order adaptive mesh method to arbitrary high order Godunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistribution algorithm and solution algorithm. The mesh-redistribution algorithm is derived based on variational approach, while a new solution algorithm is developed to preserve high order numerical accuracy well. The feature of proposed Adaptive ADER scheme includes that 1). all simulations in this paper are stable for large CFL number, 2). third order convergence of the numerical solutions is successfully observed with adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions are obtained successfully when there are shocks in the solution. A variety of numerical examples show the feature well.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2016-0088}, url = {http://global-sci.org/intro/article_detail/cicp/9983.html} }
TY - JOUR T1 - A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws AU - Yaguang Gu & Guanghui Hu JO - Communications in Computational Physics VL - 3 SP - 829 EP - 851 PY - 2017 DA - 2017/09 SN - 22 DO - http://doi.org/10.4208/cicp.OA-2016-0088 UR - https://global-sci.org/intro/article_detail/cicp/9983.html KW - AB -

We introduce a third order adaptive mesh method to arbitrary high order Godunov approach. Our adaptive mesh method consists of two parts, i.e., mesh-redistribution algorithm and solution algorithm. The mesh-redistribution algorithm is derived based on variational approach, while a new solution algorithm is developed to preserve high order numerical accuracy well. The feature of proposed Adaptive ADER scheme includes that 1). all simulations in this paper are stable for large CFL number, 2). third order convergence of the numerical solutions is successfully observed with adaptive mesh method, and 3). high resolution and non-oscillatory numerical solutions are obtained successfully when there are shocks in the solution. A variety of numerical examples show the feature well.

Yaguang Gu and Guanghui Hu. (2017). A Third Order Adaptive ADER Scheme for One Dimensional Conservation Laws. Communications in Computational Physics. 22 (3). 829-851. doi:10.4208/cicp.OA-2016-0088
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