2-D H-Adaptive Finite Element Method for Gas Gun Design

2003 ◽  
Author(s):  
Timothy T. deBues ◽  
Darrell W. Pepper ◽  
Yitung Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Outer Surface ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Gas Gun ◽  
First Case ◽  
Tube Exit ◽  
Launch Tube ◽  
Element Method

The Joint Actinide Shock Physics Experimental Research (JASPER) facility utilizes a two-stage light gas gun to conduct equation of state experiments. The gun has a launch tube bore diameter of 28 mm, and is capable of launching projectiles at a velocity of 7.5 km/s using compressed hydrogen as a propellant. A numerical study is conducted to determine the effects that launch tube exit geometry changes have on attitude of the projectile in flight. A comparison of two launch tube exit geometries is considered. The first case is standard muzzle geometry where the wall of the bore and the outer surface of the launch tube form a right angle. The second case includes a beveled transition from the wall of the bore to the outer surface of the launch tube. An h-adaptive, Petrov-Galerkin finite element method is employed to model the axisymmetric compressible flow equations. Numerical solutions indicate that pressure variations occur on the back face of the projectile from case to case.

Numerical Modeling of Unsteady Gas Flow Around the Projectile in the Light Gas Gun

2004 ◽  
Author(s):  
Valery Ponyavin ◽  
Yitung Chen ◽  
Darrell W. Pepper ◽  
Hsuan-Tsung Hsieh
Keyword(s):  
Outer Surface ◽  
Gas Flow ◽  
Gas Gun ◽  
Gun Barrel ◽  
First Case ◽  
Tube Exit ◽  
Volume Method ◽  
Unsteady Gas Flow ◽  
Velocity Pressure ◽  
Launch Tube

In this study, an attempt to calculate the characteristics of gas flow around a projectile during the motion of the projectile in the Joint Actinide Shock Physics Experimental Research (JASPER) light-gas gun is undertaken. The flow is considered as axisymmetric, nonstationary, nonisothermal, compressible, and turbulent. For calculating the flow around the projectile, the finite volume method was employed. A comparison between two launch tube exit geometries was made. The first case was standard muzzle geometry, where the wall of the bore and the outer surface of the launch tube form a 90 degree angle. The second case included a 26.6 degree bevel transition from the wall of the bore to the outer surface of the launch tube. The results of the calculations are represented in figures depicting the flow at different moments of time. The figures show the fields of velocity, pressure and density, as well as the appearance of shock waves inside the geometry. Some comparisons with calculations of the same problem but using finite-element method were made. The obtained results can be further used for optimization JASPER geometry. The results also can be used for calculating the gun barrels for the strength and the oscillatory stability. In our future study we will couple structural analysis of the gun barrel material with the gas dynamic calculation of motion of the projectile in the gun barrel with the use of advanced computational methods.

scholarly journals Numerical study of Fisher's equation by a Petrov-Galerkin finite element method

1991 ◽  
Vol 33 (1) ◽  
pp. 27-38 ◽  
Author(s):  
S. Tang ◽  
R. O. Weber
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Study ◽  
Galerkin Finite Element Method ◽  
Linear Diffusion ◽  
Galerkin Finite Element ◽  
Fisher’S Equation ◽  
Nonlinear Reaction ◽  
Fisher's Equation ◽  
Element Method

AbstractFisher's equation, which describes a balance between linear diffusion and nonlinear reaction or multiplication, is studied numerically by a Petrov-Galerkin finite element method. The results show that any local initial disturbance can propagate with a constant limiting speed when time becomes sufficiently large. Both the limiting wave fronts and the limiting speed are determined by the system itself and are independent of the initial values. Comparing with other studies, the numerical scheme used in this paper is satisfactory with regard to its accuracy and stability. It has the advantage of being much more concise.

Hybrid Nodal Integral / Finite Element Method for Time-Dependent Convection Diffusion Equation

2021 ◽  
Author(s):  
Sundar Namala ◽  
Rizwan Uddin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Numerical Solutions ◽  
Second Order ◽  
Time Dependent ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Integral Methods ◽  
Element Method

Abstract Nodal integral methods (NIM) are a class of efficient coarse mesh methods that use transverse averaging to reduce the governing partial differential equation(s) (PDE) into a set of ordinary differential equations (ODE). The standard application of NIM is restricted to domains that have boundaries parallel to one of the coordinate axes/palnes (in 2D/3D). The hybrid nodal-integral/finite-element method (NI-FEM) reported here has been developed to extend the application of NIM to arbitrary domains. NI-FEM is based on the idea that the interior region and the regions with boundaries parallel to the coordinate axes (2D) or coordinate planes (3D) can be solved using NIM, and the rest of the domain can be discretized and solved using FEM. The crux of the hybrid NI-FEM is in developing interfacial conditions at the common interfaces between the NIM regions and FEM regions. We here report the development of hybrid NI-FEM for the time-dependent convection-diffusion equation (CDE) in arbitrary domains. Resulting hybrid numerical scheme is implemented in a parallel framework in Fortran and solved using PETSc. The preliminary approach to domain decomposition is also discussed. Numerical solutions are compared with exact solutions, and the scheme is shown to be second order accurate in both space and time. The order of approximations used for the development of the scheme are also shown to be second order. The hybrid method is more efficient compared to standalone conventional numerical schemes like FEM.

Linearization of the finite element method for gradient flows by Newton’s method

2020 ◽  
Author(s):  
Georgios Akrivis ◽  
Buyang Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Newton’S Method ◽  
Newton's Method ◽  
Numerical Solutions ◽  
Resolvent Estimate ◽  
Optimal Order ◽  
Gradient Flows ◽  
The Finite Element Method ◽  
Element Method

Abstract The implicit Euler scheme for nonlinear partial differential equations of gradient flows is linearized by Newton’s method, discretized in space by the finite element method. With two Newton iterations at each time level, almost optimal order convergence of the numerical solutions is established in both the $L^q(\varOmega )$ and $W^{1,q}(\varOmega )$ norms. The proof is based on techniques utilizing the resolvent estimate of elliptic operators on $L^q(\varOmega )$ and the maximal $L^p$-regularity of fully discrete finite element solutions on $W^{-1,q}(\varOmega )$.

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