首页> 外文学位 >The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws.
【24h】

The discontinuous finite element method with the Taylor-Galerkin approach for nonlinear hyperbolic conservation laws.

机译:非线性双曲守恒律的泰勒-加勒金方法的不连续有限元方法。

获取原文
获取原文并翻译 | 示例

摘要

A one step, explicit finite element scheme which is second order accurate in both time and space is developed for the computation of weak solutions of nonlinear hyperbolic conservation laws. The scheme is an improved version of the discontinuous finite element (Discontinuous Galerkin) method using the Taylor-Galerkin procedure. It is linearly stable under a fixed CFL number up to nearly 0.4 (or {dollar}1over2{dollar} for the alternative two step explicit scheme also developed here) and TVDM which guarantees convergence to a weak solution in non-linear problems when the flux limiter is applied with the CFL number up to 0.366 (or {dollar}1over2{dollar} for the two step scheme) in one dimension. The scheme is easily extended to multi-dimensions by approximating the two-dimensional Riemann problem and using the extended flux limiter. No special treatment is required for the refined elements when using an adaptive finite element method. Numerical experimentation demonstrates the overall improvement in solution quality and the convergence of the solution to the entropy one even for non-convex flux cases. The scheme captures stationary dicontinuities perfectly.
机译:为计算非线性双曲守恒律的弱解,开发了一种在时间和空间上都是二阶精确的一步式显式有限元方案。该方案是使用Taylor-Galerkin程序的不连续有限元(Discontinuous Galerkin)方法的改进版本。它在高达近0.4的固定CFL数下也线性稳定(对于此处也开发的替代两步显式方案,则为{dollar} 1over2 {dollar})和TVDM保证了通量为通量时非线性问题的弱解的收敛性一维应用的限制器的CFL值最高为0.366(对于两步方案,则为{dollar} 1over2 {dollar})。通过近似二维Riemann问题并使用扩展的通量限制器,可以将该方案轻松扩展到多维。使用自适应有限元方法时,精炼元素不需要特殊处理。数值实验表明,即使在非凸通量情况下,溶液质量也得到了整体改善,并且解决方案收敛于熵。该方案完美地捕获了平稳不连续性。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱:kefu@zhangqiaokeyan.com

京公网安备:11010802029741号 ICP备案号:京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有
  • 客服微信

  • 服务号