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As discussed in Chap.  1 , the nonlinear conservation laws support shock waves as their solution. As a result, in approximating shock waves and other discontinuities, appropriate spatial discretizations are needed to avoid spurious oscillations near discontinuities that do not diminish with grid refinement. To remedy the spurious oscillations, we have introduced in Chap.  2 nonlinear schemes based on weighted essentially nonoscillatory (WENO) and targeted essentially nonoscillatory (TENO)Targeted Essentially Non-Oscillatory (TENO) schemes that are high-order accurate and offer simplicity and generality.

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High-Order Nonlinear Schemes for Nonlinear Conservation Laws

  • 章节

  • 发表日期：

    2025年

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  • Khosro Shahbazi

摘要

As discussed in Chap.  1 , the nonlinear conservation laws support shock waves as their solution. As a result, in approximating shock waves and other discontinuities, appropriate spatial discretizations are needed to avoid spurious oscillations near discontinuities that do not diminish with grid refinement. To remedy the spurious oscillations, we have introduced in Chap.  2 nonlinear schemes based on weighted essentially nonoscillatory (WENO) and targeted essentially nonoscillatory (TENO)Targeted Essentially Non-Oscillatory (TENO) schemes that are high-order accurate and offer simplicity and generality.