A mathematical model is developed of a spring-loaded pressure relief valve connected to a reservoir of compressible fluid via a single, straight pipe. The valve is modelled using Newtonian mechanics, under assumptions that the reservoir pressure is sufficient to ensure choked flow conditions. The usual assumptions of ideal gas theory lead to a system of first-order partial differential equation...

We develop a high order numerical boundary condition for compressible inviscid flows involving complex moving geometries. It is based on finite difference methods on fixed Cartesian meshes which pose a challenge that the moving boundaries intersect the grid lines in an arbitrary fashion. Our method is an extension of the so-called inverse Lax-Wendroff procedure proposed in [16] for conservation...

Abstract. In this paper, we give a survey and discuss new developments and computational results for a high order accurate numerical boundary condition based on finite difference methods for solving hyperbolic equations on Cartesian grids, while the physical domain can be arbitrarily shaped. The challenges are the wide stencil for the high order scheme and the fact that the physical boundary do...

We present a solver of 3D two-fluid plasma model for the simulation short-pulse laser interactions with plasma. This resolves equations ideal gas closure. also include Bhatnagar-Gross-Krook collision model. Our is based on PseudoSpectral Time-Domain (PSTD) method to solve Maxwell's curl equations. use Strang splitting integrate Euler source term: while are solved composite scheme mixing Lax-Fri...

This work introduces a single-stage, single-step method for the compressible Euler equations that is provably positivitypreserving and can be applied on both Cartesian and unstructured meshes. This method is the first case of a singlestage, single-step method that is simultaneously high-order, positivity-preserving, and operates on unstructured meshes. Time-stepping is accomplished via the Lax-...

Goal of this thesis is to study four problems. In chapters 3-5, we consider scalar conservation law in one space dimension with strictly convex flux. First problem is to know the profile of the entropy solution. In spite of the fact that, this was studied extensively in last several decades, the complete profile of the entropy solution is not well understood. Second problem is the exact control...

A well-known theorem of Lax and Wendroff states that if the sequence of approximate solutions to a system of hyperbolic conservation laws generated by a conservative consistent numerical scheme converges boundedly a.e. as the mesh parameter goes to zero, then the limit is a weak solution of the system. Moreover, if the scheme satisfies a discrete entropy inequality as well, the limit is an entr...