Geodesic
A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations
Applications of Mathematics, Tome 64 (2019) no. 5, pp. 531-556 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order time discretization of a perturbed system which approximates the MHD system. The main results are that the convergence for the velocity and the magnetic field are strongly second-order in time while that for the pressure is strongly first-order in time. Some numerical tests are performed to illustrate the theoretical predictions and demonstrate the efficiency of the proposed scheme.\looseness -1
A higher order pressure segregation scheme for the time-dependent incompressible magnetohydrodynamics (MHD) equations is presented. This scheme allows us to decouple the MHD system into two sub-problems at each time step. First, a coupled linear elliptic system is solved for the velocity and the magnetic field. And then, a Poisson-Neumann problem is treated for the pressure. The stability is analyzed and the error analysis is accomplished by interpreting this segregated scheme as a higher order time discretization of a perturbed system which approximates the MHD system. The main results are that the convergence for the velocity and the magnetic field are strongly second-order in time while that for the pressure is strongly first-order in time. Some numerical tests are performed to illustrate the theoretical predictions and demonstrate the efficiency of the proposed scheme.\looseness -1
DOI : 10.21136/AM.2019.0069-17
Classification : 65N12, 65N15, 65N30
Keywords: magnetohydrodynamics equations; pressure segregation method; higher order scheme; stability; error estimate 
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     title = {A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations},
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Yang, Yun-Bo; Jiang, Yao-Lin; Kong, Qiong-Xiang. A higher order pressure segregation scheme for the time-dependent magnetohydrodynamics equations. Applications of Mathematics, Tome 64 (2019) no. 5, pp. 531-556. doi: 10.21136/AM.2019.0069-17

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