Scientific computing topics under current study

1
Scientific computing topics under current study

• Tony W. H. Sheu
• Scientific Computing and Cardiovascular
  Simulation Lab.
• Computational Mechanics and Scientific
  Visualization Lab.
• National Taiwan University
• TEL [phone] FAX [phone]
• E-mail twhsheu_at_ntu.edu.tw
• http//ccms.ntu.edu.tw/twhsheu

Dec. 8. 2010 in NTU for the interaction of CQSE
and TIMS colleagues
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Contents

• (1) Nonlinear partial differential equations
• 1.1 Westervelt equation
• 1.2 Camassa-Holm equation
• 1.3 Schrodinger equation
• (2) Nonlinear system of partial differential
  equations for
• incompressible fluid flow
• 2.1 Incompressible Navier-Stokes ( NS )
  equations

Coupled with magnetic induction equation
Magnetohydrodynamic ( MHD ) equations
Coupled with electric field equation
Electrohydrodynamic ( EHD ) equations
Coupled with ion transport equation
Electrosmotic flow ( EOF ) equations
Free ( interface ) flow equations
Coupled with level-set equation
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• 2.2 Subgrid models for the simulation of flow
  turbulence
• - Leray-a differential model
• - NS-a differential model
• - NS-? differential model
• (3) Maxwells equations
• (4) Applications
• High-intensity focussed ultrasound ( HIFU ) for
  liver tumor
• ablation
• Inspiration / expiration in human lung airway
• Construction of acupuncture ( ? ) moxibustion (
  ? ) model
• Free surface flow over an irregular obstacle

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1. Nonlinear partial differential equations

• (A) Westervelt equation ( one-manpower )
• - Challenge Computationally efficient
  linearization of the last
• term in case of a
  focused high-frequency and
• sound field
• - Application Coupled with the hydrodynamics
  and
• energy equations in
  HIFU study

Linear wave
Absorption contribution
Nonlinear contribution
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• (B) Camassa-Holm equation ( 1/3 manpower )
• - Academic topics under investigation
• Resolve oscillations due to the highly dispersive
  term
• so as to capture the cusp ( peakon or
  soliton ) profile
• Clarify the debate if the dissipative behavior is
  present in the peakon-antipeakon problem
• Preserve Hamiltonians embedded in the above
  equation

Mixed derivative term
Three nonlinear terms
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• (C) Schrodinger equation ( one manpower )
• - Academic topics under investigation
• Preserve the Hamiltonian
• and the particle number
  properties imbedded in the above equation
• Explore the time-evolving behavior of the
  momentum given by

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2. Nonlinear system of Partial differential
equations
(2.1) Incompressible Navier-Stokes ( NS )
equations

• (A) Incompressible MHD equations ( 1/3 manpower )

Note For electrically conducting fluids such as
the plasma and Liquid metal
Hydrodynamic field equations
Magnetic field equations
Academic topics under current investigation
- enforce divergence-free condition
for the momentum equations - enforce
divergence-free condition for the
magnetic induction equations
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• (B) Incompressible EHD equations ( one manpower )

Note For electrically charged fluids
Hydrodynamic field equations
Electric field equations
Academic topics under current investigation -
Reveal the bifurcation types and the route to
chaos in the unipolar injection problem
- Resolve sharp solution profile in the EHD flow
field
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• (C) Incompressible EOF (??) equations ( 1/3
  manpower )

Note For the fluid with ion
Hydrodynamic equations
Energy equation
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Electrosmotic equations
Academic topic under current investigation -
Simulation of the 3D large-scale EOF microchannel
flow problem in parallel CPU and GPU
processors
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• (D) Incompressible Interface / free surface flow
  equations
• ( one man power )

Academic topics under current investigation -
Preserve either the area or volume of the liquid
and gas phases - Resolve contact
discontinuity oscillations near the
interface/free surface
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(2.2) Subgrid turbulence models ( one manpower )
(A) Leray-a regularized model
where
(C) NS-? regularized model
(B) NS-a regularized model
Academic topic under current investigation -
Examine how well these regularized NS equations
can be applied to model flow turbulence
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3. Maxwell equations ( two manpower )
Academic topics under current investigation -
Preserve Hamiltonians and conserved quantities
- Enforce Gauss law ( divergence-free conditions
for and , or
) - Preserve symplecticity and energy in
the above equations - Optimize the numerical
dispersion relation
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4. Applications
(A) High-intensity focused ultrasound ( HIFU ) of
liver tumor ablatian
The time-evolving volume with the temperature
higher than 45 C in the liver tumor
(ultrasound is imposed in the first 5 seconds)
Animation
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4. Applications
(B) Inspiration / expiration in human lung airways
Velocity profile
Expiration
Inspiration
Inlet flow profile
Pressure contours
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4. Applications
(C) Construction of acupuncture ( ? )
moxibustion ( ? ) model
Acupuncture needle is combined with one-column
needle and one curl handle, which covers on the
columned needle.
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Temperature distribution on the calf due to
moxibustion practice
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4. Applications
(D) Free surface flow over an irregular obstacle