Nonlinear Spectral Analysis in a Multiply-Connected Region

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The spectral difference scheme is very effective to numerical analysis for nonlinear partial differential equations, such as Navier-Stokes equations. Effectiveness has been extended, using a conformal mapping with doubly-periodic functions.Target equations are mainly partial differential equations with boundary values and/or initial values.In this project, triply-connected two-dimensional regions or axisymmetric doubly-connected regions are treated. At the first stage, fluid is assumed to be Newtonian.(i) Various conformal mapping function are introduced.(ii) Various configurations are treated.(iii) Region of infinite extension, non-isothermal boundary, and natural convection is treated.As a result, conformal mapping using Jacobian elliptic functions is found to be very effective in multiply-connected region under a spectral finite difference scheme.