Numerical Simulation of One-dimensional Wave Runup by CIP-like Moving Boundary Condition Koji FUJIMA National Defense Academy of Japan.

Slides:

Advertisements

Similar presentations

Outline Overview of Pipe Flow CFD Process ANSYS Workbench

Advertisements

RAMS/BRAMS Basic equations and some numerical issues.

An Analysis of Hiemenz Flow E. Kaufman and E. Gutierrez-Miravete Department of Engineering and Science Rensselaer at Hartford.

1 Simulation of Micro-channel Flows by Lattice Boltzmann Method LIM Chee Yen, and C. Shu National University of Singapore.

CE33500 – Computational Methods in Civil Engineering Differentiation Provided by : Shahab Afshari

Session: Computational Wave Propagation: Basic Theory Igel H., Fichtner A., Käser M., Virieux J., Seriani G., Capdeville Y., Moczo P.  The finite-difference.

Chapter 18 Interpolation The Islamic University of Gaza

Aspects of Conditional Simulation and estimation of hydraulic conductivity in coastal aquifers" Luit Jan Slooten.

Combating Dissipation. Numerical Dissipation  There are several sources of numerical dissipation in these simulation methods  Error in advection step.

Adnan Khan Lahore University of Management Sciences Peter Kramer Rensselaer Polytechnic Institute.

Peyman Mostaghimi, Martin Blunt, Branko Bijeljic 11 th January 2010, Pore-scale project meeting Direct Numerical Simulation of Transport Phenomena on Pore-space.

An Optimal Nearly-Analytic Discrete Method for 2D Acoustic and Elastic Wave Equations Dinghui Yang Depart. of Math., Tsinghua University Joint with Dr.

A posteriori Error Estimate - Adaptive method Consider the boundary value problem Weak form Discrete Equation Error bounds ( priori error )

Combining the strengths of UMIST and The Victoria University of Manchester Aspects of Transitional flow for External Applications A review presented by.

A reaction-advection-diffusion equation from chaotic chemical mixing Junping Shi 史峻平 Department of Mathematics College of William and Mary Williamsburg,

An Optimal Learning Approach to Finding an Outbreak of a Disease Warren Scott Warren Powell

Shallow water equations in 1D: Method of characteristics

Combined Lagrangian-Eulerian Approach for Accurate Advection Toshiya HACHISUKA The University of Tokyo Introduction Grid-based fluid.

Generation of Solar Energetic Particles (SEP) During May 2, 1998 Eruptive Event Igor V. Sokolov, Ilia I. Roussev, Tamas I. Gombosi (University of Michigan)

Modeling Fluid Phenomena -Vinay Bondhugula (25 th & 27 th April 2006)

Computations of Fluid Dynamics using the Interface Tracking Method Zhiliang Xu Department of Mathematics University of Notre.

Chapter 6 Numerical Interpolation

Numerical Methods for Partial Differential Equations

Modeling, Simulating and Rendering Fluids Thanks to Ron Fediw et al, Jos Stam, Henrik Jensen, Ryan.

Finite Differences Finite Difference Approximations  Simple geophysical partial differential equations  Finite differences - definitions  Finite-difference.

Erin Catto Blizzard Entertainment Numerical Integration.

A Hybrid Particle-Mesh Method for Viscous, Incompressible, Multiphase Flows Jie LIU, Seiichi KOSHIZUKA Yoshiaki OKA The University of Tokyo,

Introduction This chapter gives you several methods which can be used to solve complicated equations to given levels of accuracy These are similar to.

Animation of Fluids.

A Novel Wave-Propagation Approach For Fully Conservative Eulerian Multi-Material Simulation K. Nordin-Bates Lab. for Scientific Computing, Cavendish Lab.,

1 Discretization of Fluid Models (Navier Stokes) Dr. Farzad Ismail School of Aerospace and Mechanical Engineering Universiti Sains Malaysia Nibong Tebal.

Assimilation of HF Radar Data into Coastal Wave Models NERC-funded PhD work also supervised by Clive W Anderson (University of Sheffield) Judith Wolf (Proudman.

1 Interpolation. 2 What is Interpolation ? Given (x 0,y 0 ), (x 1,y 1 ), …… (x n,y n ), find the value of ‘y’ at a.

A conservative FE-discretisation of the Navier-Stokes equation JASS 2005, St. Petersburg Thomas Satzger.

A particle-gridless hybrid methods for incompressible flows

COMPARISON OF ANALYTICAL AND NUMERICAL APPROACHES FOR LONG WAVE RUNUP by ERTAN DEMİRBAŞ MAY, 2002.

Remember that given a position function we can find the velocity by evaluating the derivative of the position function with respect to time at the particular.

Introduction to Level Set Methods: Part II

Grid or Mesh or Adaptive Procedure Fluid Dynamics is Made for This And this was developed in the Early 1970s.

Akram Bitar and Larry Manevitz Department of Computer Science

Ale with Mixed Elements 10 – 14 September 2007 Ale with Mixed Elements Ale with Mixed Elements C. Aymard, J. Flament, J.P. Perlat.

Three-Dimensional MHD Simulation of Astrophysical Jet by CIP-MOCCT Method Hiromitsu Kigure (Kyoto U.), Kazunari Shibata (Kyoto U.), Seiichi Kato (Osaka.

Materials Process Design and Control Laboratory Sibley School of Mechanical and Aerospace Engineering 169 Frank H. T. Rhodes Hall Cornell University Ithaca,

HEAT TRANSFER FINITE ELEMENT FORMULATION

Data Modeling Patrice Koehl Department of Biological Sciences National University of Singapore

Interactive Graphics Lecture 10: Slide 1 Interactive Computer Graphics Lecture 10 Introduction to Surface Construction.

1 INTERPOLASI. Direct Method of Interpolation 3 What is Interpolation ? Given (x 0,y 0 ), (x 1,y 1 ), …… (x n,y n ), find the value of ‘y’ at a value.

This chapter is concerned with the problem in the form Chapter 6 focuses on how to find the numerical solutions of the given initial-value problems. Main.

Solving Partial Differential Equation Numerically Pertemuan 13 Matakuliah: S0262-Analisis Numerik Tahun: 2010.

Quadrature – Concepts (numerical integration) Don Allen.

Advanced Numerical Techniques Mccormack Technique CFD Dr. Ugur GUVEN.

EEE 431 Computational Methods in Electrodynamics

Reporter: Prudence Chien

Modeling of Traffic Flow Problems

Kazushi Takemura, Ishioka Keiichi, Shoichi Shige

Chamber Dynamic Response Modeling

Overview of Molecular Dynamics Simulation Theory

Mathematical modeling of cryogenic processes in biotissues and optimization of the cryosurgery operations N. A. Kudryashov, K. E. Shilnikov National Research.

Sahar Sargheini, Alberto Paganini, Ralf Hiptmair, Christian Hafner

Numerical Model Atmospheres (Hubeny & Mihalas 16, 17)

Chapter 10. Numerical Solutions of Nonlinear Systems of Equations

Numerical Solutions of Partial Differential Equations

Investigators Tony Johnson, T. V. Hromadka II and Steve Horton

Section 11 Lecture 2: Analysis of Supersonic Conical Flows

TWO STEP EQUATIONS 1. SOLVE FOR X 2. DO THE ADDITION STEP FIRST

Solving Multi Step Equations

Solving Multi Step Equations

Akram Bitar and Larry Manevitz Department of Computer Science

Presentation transcript:

Numerical Simulation of One-dimensional Wave Runup by CIP-like Moving Boundary Condition Koji FUJIMA National Defense Academy of Japan

Cubic-Interpolated Pseudo-particle [Yabe; 1988, 1991] Basic Idea (1) : pseudo-particle The Solution of can be approximated as Basic Idea (2) : cubic-polynomial interpolation in is interpolated by cubic-polynomial by using, where f’ is the derivative with respect to x.

CIP algorithm for Phase 1 = non-advection phase Phase 2 = advection phase Pseudo-particle Cubic-polynomial Interpolation

FEM + CIP (Ishikawa et al., 2003)

CIP method Very easy and applicable to solve the various hyperbolic equations (one-dimensional, multi- dimensional, one-variable, multi-variables,,,) All variables are defined usually at the same time step.

The present method The main part of simulation is same as the conventional method. (Staggered leapflog mesh) Moving boundary (wave front) is evaluated by CIP-like (pseudo-particle) manner. FEM+CIP seems too heavy for the practical tsunami simulation. The conventional tsunami simulation has sufficient cost-performance for many problems.

Moving Boundary in the Conventional method When, M=0 and the wave front does not move. When, M is computed and the wave front moves.

Numerical scheme of the present model: ( and are assumed to be determined) Equation of continuity : extrapolated by u behind the wave front

Equation of motion The advection and pressure gradient terms are evaluated by the same manner as the conventional tsunami simulation. When M behind the front is computed, pressure gradient is estimated as the right figure.

Extrapolation of Cubic-extrapolation Linear-extrapolation Same as closest grid The simplest method is adopted.

Wave profile and velocity distribution at t=160s

Wave profile and velocity distribution at t=175s

Wave profile and velocity distribution at t=220s

Trajectory of wave front location and front velocity x(numerical), x(theoretical) u(numerical), u(theoretical)

Trajectory of wave front location and front velocity x(numerical-conventional model), x(theoretical) u(numerical-conventional model), u(theoretical)

Summary The only difference of the conventional model and the present model is the treatment of the moving boundary. The computation cost is almost similar in both models, although those results are quite different. The conventional model underestimates the wave runup and rundown. The present model tend to underestimate the wave rundown and overestimate the wave runup.