A discontinuous Galerkin method for mathematical simulating of gas-liquid mixture flows

Abstract

We present mathematical simulating results of a gas-liquid mixture flow in a cylindrical pipe. The gas-liquid mixture consists of the mineralized water and propane gas. To analyze the mineral composition of the fluid, a sensor is mounted in the pipe. The sensor affects the topology of the flow velocity vector field. The gas-liquid mixture flow is described by the unsteady Navier-Stokes equations. When the flow rate of gas-liquid mixtures exceeds 20 m/s, eddy flows occur in the pipe with obstacles. A method of discretization should take into account the problem specifics: rapidly changing gradients, the prevalence of the convective term in the Navier-Stokes equations. A computational scheme of discontinuous Galerkin method has the local conservative property and is best suited for solving such singularly perturbed problems. To perform a spatial discretization, a computational scheme of the discontinuous Galerkin method in the function spaces H(div) and L 2 is used. Application of the multiscale approach allows breaking down the solution of the simulation problem into several smaller ones that can be solved using parallel computations. Mathematical modeling results of the gas-liquid mixture flow in the pipe with different options for the sensor location are presented.