TEST CASE DOCUMENTATION

AND TESTING RESULTS

TEST CASE ID CESE-VER-1.1

1-D Shock Tube Problem

Tested with LS-DYNA R v980 Revision Beta

Friday 1st June, 2012

 Document Information
Confidentiality external use
Document Identifier LSTC-QA-LS-DYNA-CESE-VER-1.1-1
Author(s) Iñaki Çaldichoury, Zeng Chan Zhang
Number of pages 7
Date created Friday 1st June, 2012
Distribution External

Disclaimer:
The test case(s) described herein are for illustrative purposes only. LSTC
does not warrant that a user of these or other LS-DYNA features will expe-
rience the same or similar results or that a feature will meet the user’s par-
ticular requirements or operate error free. FURTHERMORE, THERE ARE
NO WARRANTIES, EITHER EXPRESS OR IMPLIED, ORAL OR WRIT-
TEN, WITH RESPECT TO THE DOCUMENTATION AND SOFTWARE
DESCRIBED HEREIN INCLUDING, BUT NOT LIMITED TO ANY IM-
PLIED WARRANTIES (i) OF MERCHANTABILITY, OR (ii) FITNESS
FOR A PARTICULAR PURPOSES, OR (iii) ARISING FROM COURSE
OF PERFORMANCE OR DEALING, OR FROM USAGE OF TRADE OR.
THE REMEDIES SET FORTH HEREIN ARE EXCLUSIVE AND IN LIEU
OF ALL OTHER REMEDIES FOR BREACH OF WARRANTY.

LSTC-QA-LS-DYNA-CESE-VER-1.1-1 i
Contents
1 Introduction 1
1.1 Purpose of this Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2 Test Case Information 2

3 Test Case Specification 3

3.1 Test Case Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.2 Test Case Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3.3 Model Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

4 Test Case Results 6

4.1 Test Case observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

ii LSTC-QA-LS-DYNA-CESE-VER-1.1-1
1 Introduction
1.1 Purpose of this Document
This document specifies the test case CESE-VER-1.1. It provides general test case informa-
tion like name and ID as well as information to the confidentiality, status, and classification
of the test case.

A detailed description of the test case is given, the purpose of the test case is defined, and the
tested features are named. Results and observations are stated and discussed. Testing results
are provided in section 4.1 for the therein mentioned LS-DYNA R version and platforms.

LSTC-QA-LS-DYNA-CESE-VER-1.1-1 1
2 Test Case Information

Test Case Summary

Confidentiality external use

Test Case Name 1-D Shock Tube Problem
Test Case ID CESE-VER-1.1
Test Case Status Under consideration
Test Case Classification Verification
Metadata SHOCK WAVES

Table 1: Test Case Summary

2 LSTC-QA-LS-DYNA-CESE-VER-1.1-1
3 Test Case Specification
3.1 Test Case Purpose
This is a classic 1-D model, introduced by G.A. Sod [2] and its purpose is to verify the ability
of the CESE solver to solve fluid dynamics problems with shock wave behavior.

3.2 Test Case Description

Driver Section Driven Section

High Pressure Zone Zone Low Pressure

P4, ρ4, Cp4, Cv4 4 1 P1, ρ1, Cp1, Cv1

Diaphragm

Figure 1: Initial state in the shock tube

Shock tubes have many important applications in the study of high-temperature gases in
physics and chemistry [1] and are frequently used in the testing of supersonic bodies and
hypersonic entry vehicles. The test case consists of a tube closed at both ends, with a
diaphragm separating a region of high-pressure gas on the left from a region of low pressure
gas on the right (see Figure (1)). When the diaphragm is removed, an expansion wave travels
to the left and a shock wave to the right (see Figure (2)). Analytical solutions exist that
permit the description of the behavior of the velocity, pressure and density variables along
the horizontal axis at a given time (see Figure (3)) [1].
Interface between the driver and
Expansion wave
driven gases moving at the velocity of
propagating to the left
the gaz behind the shock wave

Zone Zone Zone Zone

4 3 2 1

Normal Shock Wave

propagating to the right

Figure 2: Flow in a shock tube after the diaphragm is broken

LSTC-QA-LS-DYNA-CESE-VER-1.1-1 3
 Expansion wave
Shock wave
u Zone 3,2

Zone 4 Zone 1
x
Expansion wave
P
Shock wave
Zone 3,2
Zone 4 Zone 1

x
Expansion wave
ρ
Shock wave
Zone 3,2
Zone 4
Zone 1
x

Figure 3: Variation of physical properties after the diaphragm is broken

3.3 Model Description

The computational domain is [0,1] in the x direction, and 200 uniform elements are used for
the mesh. Table (2) gives the physical parameters that will be used for the driver and driven
gazes. In this test case, the flow will be considered inviscid.

4 LSTC-QA-LS-DYNA-CESE-VER-1.1-1
 Model physical parameters (dimensionless)
Zone 4 Zone 1
Initial Velodicty 0 0
Initial Fluid Density 1 0.125
Initial Pressure 1 0.1
Specific heat at constant 717.5 717.5
volume
Specific heat at constant 1004.5 1004.5
pressure

Table 2: Test Case Parameters

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4 Test Case Results
4.1 Test Case observations
Figure (4) shows the good agreement between numerical results and analytical solutions for
pressure, density and velocity at t=0.2.

Figure 4: Test Case Velocity profile

6 LSTC-QA-LS-DYNA-CESE-VER-1.1-1
References
[1] J. D. Anderson, Modern Compressible Flow with historical perspective, Mc Graw Hill,
2003.

[2] G. Sod, A survey of several finite difference methods for systems of nonlinear hyperbolic
conservation laws, J. Comput. Phys., (1978).

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