Space-time conservation element and solution element (CE/SE) method is a newly developed scheme for solving conservation laws which is different from well established conventional method such as finite difference, finite volume in both concept and methodology. The motivation of developing this new method is to tackle the disadvantages of traditional method by dividing the domain into cells containing user defined solution element and conservation element. Physical quantities of a cell are approximated by simple functions, which are continuous only inside the solution element. Also the derivatives of physical variables are treated as independent variables. So both the physical quantities and their derivatives are solved simultaneously. Because the use of simple approximation function wit...[ Read more ]

Space-time conservation element and solution element (CE/SE) method is a newly developed scheme for solving conservation laws which is different from well established conventional method such as finite difference, finite volume in both concept and methodology. The motivation of developing this new method is to tackle the disadvantages of traditional method by dividing the domain into cells containing user defined solution element and conservation element. Physical quantities of a cell are approximated by simple functions, which are continuous only inside the solution element. Also the derivatives of physical variables are treated as independent variables. So both the physical quantities and their derivatives are solved simultaneously. Because the use of simple approximation function within the solution element, the order of accuracy of CE/SE method is determined by the order of simple function that is being used inside the solution element. The use of simple function to approximate the solution also simplifies the process of solving the equation on the solid boundary. In this thesis, serveral test cases have been solved with different values of α in order to test the CE/SE method and the influence of α in the average equation. The result shows that most of the solutions solved by CE/SE method agree well with the exact solutions. The range of α which gives the best solution is estimated.