We develop a compressible magnetohydrodynamic solver to simulate the transonic flows based on an open-source computational fluid dynamics platform OpenFOAM. The solver is achieved by modifying the density-based Riemann solver rhoCentralFoamwhich adopts a central scheme and is available in OpenFOAM. To improve simulation accuracy and avoid non-physical oscillations, a specialized pressure-implicit algorithm with the splitting of operators is implemented to guarantee the incompressibility of magnetic field. The solver is benchmarked and the convergence rate is between the first and the second order. After benchmark, we apply this solver to magnetohydrodynamic simulations of intense-laser-produced plasma. The influences of uniform axial magnetic field and nonuniform coil-current-induced magnetic field on laser-produced plasma jets are investigated. With the uniform axial magnetic field, the positions of nozzle and the distance between knots are linearly related to square root of thermal over magnetic pressure. With the nonuniform magnetic field generated in the coil, knots are nonlinearly distributed in space and the nozzle position is modulated according to preliminary simulations. In the two kinds of magnetic fields, when the B-field strength is the same at coil center, the magnetic field of relatively small coils can shorten the times of forming nozzles and knots, suggesting that the coil magnetic field is equivalent to a higher uniform one. The simulations can be used as a reference for our future experiment on magnetized laser-produced plasma jet. Meanwhile, our simulation investigation shows that this magnetohydrodynamic solver is suitable for engineering calculation for laser plasma experiments and can deal with the situation with relatively complex configurations.