The objective of this thesis is to implement a three-stage low-storage explicit Runge-Kutta scheme that has classical third-order accuracy for velocities and is second-order accurate for pressure, for the numerical solution of incompressible Navier-Stokes equations in the in-house high performance CFD code MGLET. Additional order conditions for pressure appearing due to the half-explicit differential algebraic nature of the spatially discretized Navier-Stokes equations have been studied. Third-order Runge-Kutta coefficients have been derived based on two salient features: Firstly the Runge-Kutta stage pressures are second order accurate in time and secondly, the low-storage admissibility criteria for the coefficients. Using the recon- struction method, second order pressure is obtained as an interpolation of the stage pressure values. Stability and accuracy analysis for the general three-stage third-order Runge-Kutta schemes, as well as for the proposed scheme is also presented. Finally the low-storage algo- rithm for the time integration in MGLET is outlined. To validate the correctness of the scheme initial testing for Taylor-Green vortex decay prob- lem is done on a simple finite-volume code that mimics the time integration scheme of MGLET. With essential changes, the scheme is then implemented in MGLET. Validation for several test cases of decaying vortices and lid driven cavity is carried out to test the temporal convergence of velocities and pressure with the proposed scheme. Additional in- vestigation of the influence of second order accurate pressure on the accuracy of velocities and the performance of pressure-solver is carried out.     «

The objective of this thesis is to implement a three-stage low-storage explicit Runge-Kutta scheme that has classical third-order accuracy for velocities and is second-order accurate for pressure, for the numerical solution of incompressible Navier-Stokes equations in the in-house high performance CFD code MGLET. Additional order conditions for pressure appearing due to the half-explicit differential algebraic nature of the spatially discretized Navier-Stokes equations have been studied. Third-o...     »