Remembering Professor Olga Alexandrovna Ladyzhenskaya Twenty Years On

It has been approximately twenty years since Professor Olga Alexandrovna Ladyzhenskaya passed away.

An eminent mathematician and member of several Academies of Science, passed away in January 2004. Her distinguished career was marked by significant contributions to partial differential equations, particularly the Navier–Stokes equations and nonlinear elliptic and parabolic equations.

Born in 1922 in Kologriv, Russia, Ladyzhenskaya’s passion for natural sciences was ignited by her father, a high school mathematics teacher. Tragically, he was executed by the NKVD in 1937, which led to Ladyzhenskaya being barred from Leningrad State University. Despite this, she persisted and graduated with honors from high school in 1939. She eventually studied at Pokrovskii Pedagogical Institute in Leningrad and later, at Moscow State University, graduating in 1947. That same year, she married A. A. Kiselev and joined Leningrad State University for graduate studies under the guidance of S. L. Sobolev.

Ladyzhenskaya’s academic journey continued as she became a postgraduate student under V. I. Smirnov and later led a seminar on mathematical physics and boundary-value problems. In 1953, she defended her habilitation dissertation at Moscow State University and in 1954, joined the Steklov Mathematical Institute in Leningrad. There, she collaborated with notable mathematicians and contributed significantly to the field of mathematical physics.

Her research focused primarily on two areas: the Navier–Stokes equations, and nonlinear elliptic and parabolic equations. In 1951, she proved a fundamental inequality for elliptic operators and explored the convergence of the Fourier method for hyperbolic equations. Her work in the late 1950s on the multiplicative inequality led to the proof of the existence of global unique solutions for two-dimensional Navier–Stokes systems. She also collaborated with A. A. Kisielev to demonstrate global existence in three-dimensional cases for small initial data and external forces. Ladyzhenskaya’s contributions extended to proving global existence of stationary and regular axially symmetric solutions to Navier–Stokes equations.

Her investigations into the regularity and uniqueness of weak Hopf solutions were groundbreaking. She showed that if a weak solution belongs to a specific function space, it is unique and regular. These achievements, along with her other work, were detailed in her monographs on Navier–Stokes equations and in collaboration with other mathematicians on nonlinear elliptic and parabolic equations.

AIAA SciTech 2024 – Parametric Study of the Hypersonic Near-Field and Sonic Boom from Waveriders using a Fully-Parabolized Approach

Citation: King, C. B., Shepard, C. T., and Miller, S. A. E., “Parametric Study of the Hypersonic Near-Field and Sonic Boom from Waveriders using a Fully-Parabolized Approach,” AIAA SciTech, Orlando, FL, Jan. 8-12, AIAA 2024-2106, 2024. DOI: 10.2514/6.2024-2106

Abstract: A parametric study is performed to understand the relationship between volume displace- ment, lift, near-field signature, and sonic boom overpressure for variable wedge angle power-law waveriders. The width of a parametric waverider is varied for freestream Mach numbers from 5 to 7. Both near-field and sonic boom predictions are made with a fully parabolized approach. The Upwind Parabolized Navier-Stokes solver is used to spatially march the hypersonic flow- field in the streamwise direction. The waveform parameter method is used to propagate the hypersonic near-field to the ground from a fixed altitude of 15.85 km. We find the magnitude of the SPL varies with frequency as −19.7 log 𝒇 . There is a positive quasi-linear relationship between near-field and sonic boom overpressures with volume displacement. For 𝑴∞ = 7, a 150% volume increase yields 92.5% and 60.9% rises in near-field and sonic boom overpressures, respectively. The effect of losses due to thermo-viscous effects and atmospheric absorption are quantified. We show that for a waverider of volume ∀ = 4970 cm3 at 𝑴∞ = 7, these losses, predicted by PCBoom using modules PCBurg and enhanced Burgers’ decrease maximum overpressure by 41.6% and 39.5% relative to WPM, respectively.

Priestess of Delphi (Oracle or Pythia)

A twenty year dream came true this December, 2023, as I traveled to Adelaide, Australia to view John Collier’s Priestess of Delphi (1891), the Oracle, or Pythia. I was able to view the painting for two days.

I am not afraid to say that the experience was overwhelming, and I definately had tears in my eyes. I am not a religious person, but it was what I believe people experience when they have religious inspiration or revelation.

People traveled all over the world to consult the Oracle. How is my journey different?

Colors from my camera, and the gallery skylight cast a small glare, but helped illuminate canvas and brushtrokes. Overtime, the sun came and set, casting new reflections and colors, letting me see the painting in new ways. I took 500 high quality photographs of the painting with different light, angles, details, and far-away.

Artist: https://en.wikipedia.org/wiki/John_Collier_(painter)

Painting: https://www.agsa.sa.gov.au/collection-publications/collection/works/priestess-of-delphi/25000/

Thank you to the people and museum in AUS SA at the AGSA for the experience.

Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies

I completed my Acoustical Society work and returned to the United States.

Abstract: An analytical closed-form solution is presented for the aerodynamic near-field and ground signature from an axisymmetric body with a low thickness ratio. The Navier-Stokes equations are formulated as a boundary value problem that incorporates the incoming ambient flow-field and the aerodynamic properties on the body surface. The shape of the aerodynamic body is defined as a product of generalized functions. A direct solution for the density of the aerodynamic near-field, represented as a function of both space and time, is proposed through the integration of the Navier-Stokes equations in a generalized functional form. Pressure, temperature, velocity, and Mach number are then derived in the near-field. The methodology, being fully nonlinear, surpasses the traditional F-function, impulse, and hypersonic similarity theories originally developed for near-field prediction. The presentation outlines the major steps in deriving the analytical solution and provides predictions from an aerodynamic body in the near-field, along with the associated ground signature. The methodology is focused on aerodynamic bodies operating at high-speeds, ranging from the supersonic to the hypersonic regime. This research is supported by the Defense Advanced Research Project Agency, under Grant Number W911NF-21-1-0342.

Miller, S. A. E., “Analytical Closed-Form Solution of the Navier-Stokes Equations for the Aerodynamic Near-field and Sonic Boom from Axisymmetric Bodies,” Acoustical Society of America, Sydney, Australia, Dec. 4-8, 2023.

Acknowledgements: Research was sponsored by the Defense Advanced Research Project Agency (DARPA) and the Army Research Office and was accomplished under Grant Number W911NF-21-1-0342. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

Remembering Stephen Jurczyk

https://everloved.com/life-of/stephen-jurczyk/obituary/

It seems just like yesterday that I was at NASA Langley working for a short time under then Director Stephen G. Jurczyk. He passed away just recently on Thanksgiving of 2023. He helped propel my career in the later stages of my time at Langley. One thing that I appreciated a lot about Stephen Jurczyk was that he came up through the organization as an engineer. Not all NASA administrators or SES are engineers nowadays. I appreciated this fact about him, because I felt that he could understand the needs of the research staff of the center. Reading books like Engineer in Charge gave me a deep appreciate of the history of NASA, and also gave me a viewpoint that the leaders of NASA should be first and foremost learned people of science. Unfortunately, this is not so much the case today. I’m hopeful that future leaders of NASA come from backgrounds in engineering especially, instead of political appointees with degrees in economics or finance.

Another important lesson is that one should try and depart love ones with kind words, because one never knows when will be the last time someone says goodbye.

Toward Exascale Computation for Turbomachinery Flows

Citation: Yuhang Fu, Weiqi Shen, Jiahuan Cui, Yao Zheng, Guangwen Yang, Zhao Liu, Jifa Zhang, Tingwei Ji, Fangfang Xie, Xiaojing Lv, Hanyue Liu, Xu Liu, Xiyang Liu, Xiaoyu Song, Guocheng Tao, Yan Yan, Paul Tucker, Steven Miller, Shirui Luo, Seid Koric, and Weimin Zheng, “Toward Exascale Computation for Turbomachinery Flows,” Gordon Bell, High Performance Computing, Networking, Storage and Analysis (SC ’23). Association for Computing Machinery, Article 4, 2023. pp. 1-12. DOI: 10.1145/3581784.3627040 [Open Access Link via DOI]

The screenshot of Q-criteria iso-surface colored with velocity magnitude, with background contoured by pressure gradient to visualize the shock wave and pressure propagation.

Abstract: A state-of-the-art large eddy simulation code has been developed to solve compressible flows in turbomachinery. The code has been engineered with a high degree of scalability, enabling it to effectively leverage the many-core architecture of the new Sunway system. A consistent performance of 115.8 DP-PFLOPs has been achieved on a high-pressure turbine cascade consisting of over 1.69 billion mesh elements and 865 billion Degree of Freedoms. By leveraging a high-order unstructured solver and its portability to large heterogeneous parallel systems, we have progressed towards solving the grand challenge problem outlined by NASA, which involves a time-dependent simulation of a complete engine, incorporating all the aerodynamic and heat transfer components.

Updates on Tsien

I was able to find additional interesting pictures for my page on Tsien. One is with Adolf Busemann, father of swept wings and German / NASA Langley Scientist. Others are interesting like his home in Beijing. I’m currently reviewing a biography, and will make a note when finisihed.

National Air and Space Museum’s Journey Toward 2025

Appearing next month in the NASA Alumni Newsletter.

Walking on the Washington, D.C. Mall is an inspiring experience for all citizens. One might be inspired by the many memories and great institutions of our American people. Nestled as one of the most visited museums of the world is the National Air and Space Museum, just southwest of our Nation’s Capital. The museum had a partial reopening on October 14, 2022, with the west wing of its building unveiling eight new and renovated galleries. However, the east wing remains closed for renovation. The next phase of the renovation, which includes the east wing, is scheduled to be completed in 2025.

I have traveled to D.C. and have seen the entirety of the previous exhibits on display. Like many in the aerospace profession, every time I go to D.C. I visit the museum. I love seeing the new exhibits. The best part of the museum is not the exhibits themselves, but watching people from all over the world who are amazed. Here, people say, ‘we did that?’ often expressing surprise at what was accomplished in the approximately last 120 years of flight.

What is new in the western third of the museum includes:

  1. Destination Moon: This exhibition features numerous icons of space history, such as the Apollo 11 command module Columbia and Neil Armstrong’s Apollo 11 spacesuit, both of which have undergone extensive conservation in recent years.
  2. Jackie Cochran’s T-38: On display is a Northrop T-38A Talon flown by aviator Jacqueline “Jackie” Cochran, who set eight world records for speed, altitude, and distance flying in 1961 with this T-38.
  3. Walking On Other Worlds: An interactive experience that provides a seven-minute “tour” of seven different celestial bodies, offering an immersive media exhibit with a nearly 360-degree screen.
  4. Nation of Speed: A collection of vehicles built for speed.
  5. Diverse Stories: A broader story of aviation and space, like Neal Loving’s red Loving WR-3 air racer, a parachute used by Georgia “Tiny” Broadwick, and airline uniforms worn by pioneering women pilots like Emily Howell Warner, Cynthia Berkeley, and Bonnie Tiburzi.

I encourage everyone to plan a D.C. visit to see the grand opening of the entire renovated museum in 2025. It is important to make advance entry reservations before you go. A limited number of same day entry reservations can be made on their website. It is entirely free.

Armstrong’s Lunar Suit (Photo – Miller).
View of the new west gallery from the second floor (Photo – Miller).