Hi dear friends,

What are the advantages of the second-order TVD schemes over high order ENO type schemes ??? Please, give me references.

Thanks

Hi

ENO type schemes choose the appropriate stencil from some number of candidate stencils in order to find the smoothest data. For example, to reconstruct the value at the cell boundaries of cell i, it could conduct a selection process between the stencils i-2,i-1,i and i-1,i,i+1 and i,i+1,i+2. Thus, the stencil that has the smoothest data availible in it could be used. This process is helpful to avoid discontinuities that could be included in the domain. However, if the solution doesn't include discontinuities a selection process means additional computations that isn't necessary. I would suggest you to use WENO instead. It uses all of the candidate stencils by assigning a smoothness indicator to them. So cells from i-2 to i+2 could be included in the reconstruction, thus producing the higher order reconstruction. So, a possible answer for your question could be; if the solution domain will be smooth, TVD scheme would be better because of lesser computations, you can also handle discontinuities by additional tricks. And WENO is better for higher-order approximation.

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