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In this work, a simple fourth-order accurate finite volume semi-discretescheme is introduced to solve astrophysical magnetohydrodynamics (MHD) problemson Cartesian meshes. Hydrodynamic quantities like density, momentum and energyare discretised as volume averages. The magnetic field and electric fieldcomponents are discretised as area and line averages respectively, so as toemploy the constrained transport technique, which preserves the solenoidalityof the magnetic field to machine precision. The present method makes use of adimension-by-dimension approach employing a 1-D fourth-order accurate centrallyweighted essentially non-oscillatory (1D-CWENO4) reconstruction polynomial. Afourth-order accurate, strong stability preserving (SSP) Runge-Kutta method isused to evolve the semi-discrete MHD equations in time. Higher-order accuracyof the scheme is confirmed in various linear and nonlinear multi-dimensionaltests and the robustness of the method in avoiding unphysical numericalartifacts in the solution is demonstrated through several complex MHD problems.

Fourth Order Accurate Finite Volume CWENO Scheme For Astrophysical MHD Problems