In this article, the two-phase water hammer theoretical and numerical simulation are provided. A mathematical formulation is presented to describe transient one-dimensional flow of bubbly gas-liquid mixtures without phase change in an horizontal pipe. The features two-fluid model for simulating flows investigated. governing equations were obtained from mass momentum conservation laws combined w...

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...

Many of the recently developed high-resolution schemes for hyperbolic conservation laws are based on upwind di erencing. The building block of these schemes is the averaging of an approximate Godunov solver; its time consuming part involves the eld-byeld decomposition which is required in order to identify the \direction of the wind." Instead, we propose to use as a building block the more robu...

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...

In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction...

Wave propagation forward modeling is a widely used computational method in oil and gas exploration. The iterative stencil loops in such problems have broad applications in scientific computing. However, executing such loops can be highly time-consuming, which greatly limits their performance and power efficiency. In this paper, we accelerate the forward-modeling technique on the latest multi-co...

Single-stage or single-step high-order temporal discretizations of partial differential equations (PDEs) have shown great promise in delivering accuracy time with efficient use computational resources. There has been much success developing such methods for finite volume method (FVM) PDEs. The Picard Integral formulation (PIF) recently made single-stage accessible difference (FDM) discretizatio...