Computing the maximum amplification of the solution norm of differential-algebraic systems
Tóm tắt
We describe an effective approach for computing the maximum amplification of the solution norm of linear differential-algebraic systems that arise, in particular, when approximating with respect to space variables the linearized viscous incompressible flow equations for disturbances of laminar flows. In this context the square of the maximum amplification is the largest amplification of the kinetic energy of the disturbances whose knowledge is important in stability investigations and laminar-turbulent transition analysis. First, we reduce such a differential-algebraic system to an ordinary differential one. Then, the maximum amplification is computed as the matrix exponential norm for which a special low-rank approximation is used. To obtain an additional decrease in the computational cost, we use two initial differential-algebraic systems corresponding to coarse and fine grid approximations. The first one is used to compute a rough value of the maximum amplification, and the second one is used to refine the computation. We illustrate the efficiency of this approach with two sample flows of grooved-channel and boundary-layer types.
Tài liệu tham khảo
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