To find solutions to systems of conservation laws with discontinuities, weak solutions will be studied. To pick a unique weak solution one requires some additional conditions. In this thesis we...Show moreTo find solutions to systems of conservation laws with discontinuities, weak solutions will be studied. To pick a unique weak solution one requires some additional conditions. In this thesis we will see that for the Riemann problem in one spatial dimension, the Lax entropy conditions are a way to do this. By considering the Euler equations we will see that these conditions are equivalent to the second law of thermodynamics and therefore pick the physically relevant solution. Furthermore, we construct numerical solutions to a specific Riemann problem using a standard discretization method and a method based on nonlinear shocks, followed by a on discussion their strengths and weaknesses.Show less
