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The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differential equation. This note provides an analytical solution of the 2D isentropic vortex problem with explicit algebraic expressions in the special relativistic hydrodynamics and magnetohydrodynamics and extends it to the 3D case.
This paper studies high-order accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which is analogo
In this paper we present a framework which provides an analytical (i.e., infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the gravitational two-body problem. The formalism omits all singul
Multispecies contaminant transport in the Earths subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but currently
Implementing the modal method in the electromagnetic grating diffraction problem delivered by the curvilinear coordinate transformation yields a general analytical solution to the 1D grating diffraction problem in a form of a T-matrix. Simultaneously
In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the artificial boundary