TVD scheme
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(Difference between revisions)
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:<math> | :<math> | ||
TV(u^{n+1}) \le TV(u^n) | TV(u^{n+1}) \le TV(u^n) | ||
+ | </math> | ||
+ | |||
+ | The total variation of a grid function is defined as | ||
+ | |||
+ | :<math> | ||
+ | TV(u) = \sum_j | u_{j+1} - u_j| | ||
</math> | </math> | ||
Revision as of 04:05, 30 September 2005
A scheme is said to be TVD or Total Variation Diminishing if it does not increase the total variation of the solution, i.e.,
The total variation of a grid function is defined as
Note that a TVD scheme may not satisfy the entropy condition and hence can give incorrect solution. We have the following relationship between monotone, TVD and monotonicity preserving schemes,
Monotone scheme TVD scheme Monotonicity preserving scheme