A kinetic flux-vector splitting method for the shallow water magnetohydrodynamics

A space–time CESE scheme for shallow water magnetohydrodynamics equations with variable bottom topography

“…This problem has been also considered in [4,10,16,23]. In this problem, the variable bottom topography is given as The initial data are and the value of gravitational acceleration is g = 1.…”

“…This problem is taken from [4,10,16]. The initial data are Here, the division of computational domain and value of g is the same as we considered in Problem 2.…”

“…This problem was also considered in [10,[33][34][35]. The bottom topography is of the following form [10] The domain is in rectangular form This problem is also considered in [10,16]. We consider a square box of dimensions…”

“…Here, we are considering the approach by Brackbill and Barnes [15]. In literature, several authors used MHD problems with flat bottom with different numerical techniques [16][17][18][19][20][21]. In this paper, a CESE scheme is extended for the first time to solve SWMHD equations with variable bottom topography.…”

An initial boundary value problem for one-dimensional shallow water magnetohydrodynamics in the solar tachocline

“…In the literature, there are some theoretical and numerical works available for studying the shallow water magnetohydrodynamic equations (for theoretical works, see [12][13][14]; for numerical works, see [15][16][17][18][19][20]). However, as far as we know, there has been very few work on the subject of the well-posedness of the shallow water magnetohydrodynamic equations addressed in the literature.…”