Multiphysics with Electromagnetics
ADINAEM is now released. For an introduction to the capabilities and various applications of ADINAEM, refer to our previous News:
In addition to the applications shown in these News, we have, of course, constructed hundreds of verification problems for ADINAEM. Some of these are used in our verification manual. Below we give three of these problems as a further illustration of the kind of problems ADINAEM can be used for to solve.
Of course, these are small verification problems where we can compare with analytical solutions. More details on these problems are given in the verification manual.
1. Static 3D EMfields in a conducting block
In this first example, we demonstrate the use of ADINAEM to solve static 3D electromagnetic fields with the potential based A—φ formulation. As shown in Figure 1, an electric field and hence a current density are excited by imposing an electric potential difference between the top and bottom sides of the solid block. This current density in the block will excite a static magnetic field, and hence a magnetic potential across the block from the left side to the right side.
Figure 1 First problem: schematic showing boundary conditions
The plots in Figure 2 show the electric potential (left) and the magnetic vector potential (right).
We also compare the results obtained using ADINAEM with analytical results in Figure 3. The ADINAEM results agree perfectly with the theoretical values.
Figure 2 First problem: plot of electric potential (left) and magnetic vector potential (right)
Figure 3 First problem: ADINAEM and analytical results; electric potential (left) and magnetic vector potential (right)
2. Highfrequency harmonic electromagnetic field analysis of an annular block
The solution of the harmonic electric and magnetic fields in an annular block is calculated using ADINAEM with the E—H formulation, see Figure 4. The annular conducting block is immersed in a harmonic magnetic field, and an impedance boundary is imposed on the inner side of the block to simulate the electromagnetic effect of the inside material. The imposed harmonic magnetic field induces a harmonic electric field, which in turn induces a magnetic field.
Figure 4 Second problem: schematic showing boundary conditions
Figure 5 shows the real and imaginary parts of the electric field in vector plots. Figure 6 shows the real and imaginary parts of the magnetic field.
Figure 5 Second problem: electric field; real part (left) and imaginary part (right)
Figure 6 Second problem: magnetic field; real part (left) and imaginary part (right)
The ADINAEM results are also compared with analytical solutions, see Figure 7 and Figure 8. The ADINAEM results agree closely with the analytical solutions, and this even with the coarse mesh used.
Figure 7 Second problem: ADINAEM and analytical results, electric field;
real part (left) and imaginary part (right)
Figure 8 Second problem: ADINAEM and analytical results, magnetic field;
real part (left) and imaginary part (right)
3. Lorentz force in a conducting fluid; highfrequency 3D harmonic electric and magnetic fields
This multiphysics example has the same model geometry as used in the first example. However, the block contains a conducting fluid flowing upwards, as shown in Figure 9. The harmonic analysis is performed using ADINAEM with the potential based A—φ formulation. The timeaveraged Lorentz force is coupled to the CFD model to solve for the fluid flow.
Figure 9 Third problem: schematic showing boundary conditions
The plots in Figures 10 to 12 compare the ADINAEM results with theoretical results. Figure 10 gives the solution of the electric potential. Figure 11 shows the real and imaginary parts of the magnetic vector potential in the domain. Figure 12 shows plots to compare the ADINAEM results with theoretical results for the real and imaginary parts of the magnetic potential.
Figure 10 Third problem: band plot of electric potential, real part (left);
ADINAEM and analytical results (right)
Figure 11 Third problem: magnetic vector potential;
real part (left) and imaginary part (right)
Figure 12 Third problem: ADINAEM and analytical results, magnetic potential;
real part (left) and imaginary part (right)
The plots in Figure 13 show the pressure distribution along the flow direction (left); the calculated pressure in the fluid is compared with theoretical results (right). All these electromagnetic and fluid flow results show a very good match with the theoretical solutions.
Figure 13 Third problem: band plot of pressure distribution along flow direction (left);
ADINA and analytical results (right)
We are very pleased that ADINAEM is now available in the suite of ADINA programs and look forward to many interesting applications by our users!
References

C.A. Balanis, Advanced Engineering Electromagnetics, John Wiley & Sons, New York, 1989.

P.A. Davidson, An Introduction to Magnetohydrodynamics, Cambridge University Press, 2001.
Keywords:
ADINAEM, electromagnetics, multiphysics, fluid flow, static, harmonic, high frequencies, electric potential, magnetic potential, electric field, magnetic field, Lorentz force, impedance boundary
