journal article
LitStream Collection
Home
doi: 10.1002/fld.1650120803pmid: N/A
A formulation of an implicit characteristic‐flux‐averaging method for the unsteady Euler equations with real gas effects is presented. Incorporation of a real gas into a general equation of state is achieved by considering the pressure as a function of density and specific internal energy. The Ricmann solver as well as the flux‐split algorithm are modified by introducing the pressure derivatives with respect to density and internal energy. Expressions for calculating the values of the flow variables for a real gas at the cell faces are derived. The Jacobian matrices and the eigenvectors are defined for a general equation of state. The solution of the system of equations is obtained by using a mesh‐sequencing method for acceleration of the convergence. Finally, a test case for a simple form of equation of state displays the differences from the corresponding solution for an ideal gas.
doi: 10.1002/fld.1650120804pmid: N/A
In this paper, 2D steep gravity waves in shallow water are used to introduce and examine a new kind of numerical method for the solution of non‐linear problems called the finite process method (FPM). On the basis of the velocity potential function and the FPM, a numerical method for 2D non‐linear gravity waves in shallow water is described which can be applied to solve 3D problems, e.g. the wave resistance of a ship moving in deep or shallow water. The convergence is examined and a comparison with the results of other authors is made.
doi: 10.1002/fld.1650120805pmid: N/A
In pumping installations such as sewage pumping stations, where gas content and air entrainment exist, the computation of fluid pressure transients in the pipelines becomes grossly inaccurate when constant wave speed and constant friction are assumed. A numerical model and computational procedure have been developed here to better compute the fluid pressure transient in a pipeline by including the effects of air entrainment and gas evolution characteristics of the transported fluid. Free and dissolved gases in the fluid and cavitation at the fluid vapour pressure are modelled. Numerical experiments show that entrained, entrapped or released gases amplify the pressure peak, increase surge damping and produce asymmetric pressure surges. The transient pressure shows a longer period for down‐surge and a shorter period for up‐surge. The up‐surge is considerably amplified and the down‐surge marginally reduced when compared with the gas‐free case. These observations are consistent with the experimental observations of other investigators. Numerical experiments also show that the use of a variable loss factor in the pressure transient analysis produces marginally higher maximum and lower minimum pressure transients when compared with the constant‐loss‐factor model for pipelines where the pressures are above the fluid vapour pressure.
Johnsen, Matthias; Paulsen, Keith D.; Werner, Francisco E.
doi: 10.1002/fld.1650120806pmid: N/A
On the basis of the dispersion relation of the generalized linear wave equation we derive a radiation boundary condition (RBC) that explicitly incorporates the physical parameters of the governing equation into the form of the boundary condition. Using finite element techniques we investigate the properties of the generalized RBC by examining forced and unforced solutions to the telegraph and Klein‐Gordon equations in one dimension. The results show that within the limits of the physical parameters of the problem the generalized RBC is an improvement over the Sommerfeld RBC when the governing equation contains additional terms that influence the propagation. These gains are achieved without introducing any computational overhead. A two‐dimensional example suggests that the 1D findings can generalize to higher dimensions.
Cao, Yusong; Schultz, William W.; Beck, Robert F.
doi: 10.1002/fld.1650120807pmid: N/A
The concept of desingularization in three‐dimensional boundary integral computations is re‐examined. The boundary integral equation is desingularized by moving the singular points away from the boundary and outside the problem domain. We show that the desingularization gives better solutions to several problems. As a result of desingularization, the surface integrals can be evaluated by simpler techniques, speeding up the computation. The effects of the desingularization distance on the solution and the condition of the resulting system of algebraic equations are studied for both direct and indirect versions of the boundary integral method. Computations show that a broad range of desingularization distances gives accurate solutions with significant savings in the computation time. The desingularization distance must be carefully linked to the mesh size to avoid problems with uniqueness and ill‐conditioning. As an example, the desingularized indirect approach is tested on unsteady non‐linear three‐dimensional gravity waves generated by a moving submerged disturbance; minimal computational difficulties are encountered at the truncated boundary.
Showing 1 to 8 of 8 Articles