This article presents an iterative approach to solve Burgers equation based on predicted snapshots. No physical experiments or large-scale computation is required to obtain these snapshots. At the initial stage, the predicted snapshots are estimated by online computation in an artificial subspace. During each iteration cycle, updated snapshots are calculated in a low dimensional space and are served to generate reduced-order basis for the next cycle. Good correlation with results obtained from this approach and full order model can be achieved. Since this method does not need to construct a database based on precomputed snapshots, it is computationally inexpensive and stable with parameter changes. Although we focus on solving Burgers equation in this article, the method itself can be easily extended to many other dynamical problems.
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