Development of Condensing Mesh Method for Corner Domain at Numerical Simulation Magnetic System

Perepelkin E.E., Tarelkin A.A., Polyakova R.V., Kovalenko A.D.

лит, оияи

Abstract. A magnetostatic problem arises in searching for the distribution of the magnetic field generated by magnet systems of many physics research facilities, e.g., accelerators. The domain in which the boundary-value problem is solved often has a piecewise smooth boundary. In this case, numerical calculations of the problem require the consideration of the solution behavior in the corner domain. In this work we obtained the upper estimation of the magnetic field growth and propose a method of condensing the differential grid near the corner domain of vacuum in case of 3-dimensional space based on this estimation. The work estimate for the admissible growth of the magnetic field in the corner domain where is a constant, is a bounded function, and is the distance to the corner, is asymptotically obtained for the case of when . A method of condensing the differential mesh in the corner domain is proposed, which allows one to improve the calculation of field inside. The problems of creating a homogeneous map of the field of possible solenoid-type magnetic systems of the NICA installation are analyzed. The obtained map of homogeneous field is illustrated in Fig. 1 (5000 ± 5 Gs). Fig. 2 shows the distribution the module of magnetic induction on the ferromagnetic surface.

Fig. 1 Fig. 2

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[2] E.P. Zhidkov, E.E. Perepelkin. An analytical approach for Quasi-Linear Equation in Secondary Order. CMAM. Vol. 1, No. 3, Pp. 285-297 (2001)

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