自适应多重分辨率的组合ENO差分格式构造

CONSTRUCTION OF AN ADAPTIVE MULTIRESOLUTION HYBRID ENO SCHEME

以减少单步差分格式的计算量为目的,提出一类杂交高分辨率格式,它由高阶高分辨率和较低阶高分辨率的两种格式组合而成,通过引入一个具有自适应性质的开关函数使得新格式具有这样的性质:在解的强烈变化区域采用高阶格式,在解的光滑区域采用较低阶格式.从某种意义上说,本文提出的组合高分辨率格式具有自适应多重分辨率的思路.数值试验表明,这种组合高分辨率格式能有效地减少单步差分格式的计算量.

To reduce the computing time per step, a new hybrid high resolution difference scheme is constructed. The new scheme makes use of high resolution scheme or low resolution scheme through an adaptive switch function, depending on the gradient of the solution in a region. So the new scheme is adaptive and multiresolution. The results of numerical simulation show that the new scheme can effectively reduce the computing time per step.