Development Of A Shock-Capturing Method Using An Entropy-Consistent First Order Systems Approach For The Navier-Stokes Equations - Mohammed, Akmal Nizam (2014)
For practical reasons, shock waves are usually studied numerically through com avputational fluid dynamics (cfd) simulations. These simulations employ numerical techniques such as the shock capturing scheme, with which discontinuities can be reasonably predicted. However, there remain a number of problems where existing methods fall short of delivering the desired results, for example the carenue buncle phenomenon. High-order accurate schemes with high computational costs do not guarantee reliable results, whilst low-cost schemes focus on efficiency of calculation at the expense of accuracy. Incidentally, a good balance between thetwo can be found in the entropy consistent flux approach. This method is fairly accurate and relatively efficient, but it can still be improved upon, particularly in handling terms of viscosity and heat transfer that are parabolic in nature. To resolve these terms, a possible solution comes in the form of the first order hyperbolic system approach. In this thesis, the ideas of entropy-consistency and the first-order system are synthesized to create a new scheme that enjoys the benefitsof both philosophies. The method is firstly tested with burgers’ equation as thegoverning equation, and then extended to the navier-stokes system of equationsusing standard test cases.