I earned my Ph.D. from M.I.T. and M.Sc. from Caltech, both in Aerospace Engineering long ago, working with eminent professors in the mid-1970s. I joined Boeing as Senior Aerodynamicist before moving to Pratt & Whitney as Turbomachinery Manager. I would publish about twenty-five papers on supersonic flow, unsteady transonics, engine and airframe integration and hydrodynamic stability in AIAA Journal, Journal of Aircraft and Journal of Hydronautics before the thrill lurking in oil and gas exploration drew me to Houston. It was 1981. I would write, in my soon to be published autobiography, some memorable passages:

And so, I left for Texas towards the end of 1980, joining the petroleum industry for a career that spanned four decades. But during that time, I never lost sight of one challenge, the inverse problem of aerodynamics. This is simply explained. Small disturbance theory solves a "forward problem" for pressure, assuming f_xx + f_yy = 0, f_y(x,±0) = F^± ’(x) specified over chord where y^±(x) = F^±(x) describes the airfoil, Ñf ® 0 at infinity and a "jump" [f] in potential chosen to fulfill Kutta’s condition. I had observed how the streamfunction y solves the "inverse problem" using y_xx + y_yy = 0, where the airfoil geometry y^±(x) = - y(x,±0) is determined when a pressure condition y_y(x,±0) = - ½ C_p(x,±0) is prescribed along with a jump in [y] chosen to control trailing edge closure. This has profound implications. One can specify "good" pressure distributions that never separate boundary layers, or at least, hopefully. Or perhaps shock-free pressures to develop great supercritical airfoils. Furthermore, streamfunction formulations are almost identical to potential models, so that software development is minimal. Moreover, f and y are related by Cauchy-Riemann conditions, hence, complex variables and century-old math would produce useful results in no time. At the time, few shared my enthusiasm. But Houston came calling, so I left. And my search for elegant inverse methods became a mere life-long obsession.

That would be my first paper published in the prestigious ASME J. Applied Mech, one receptive to new mathematical ideas, written after I left the aerospace industry. This research proposed novel linear inverse methods, plus dualities connecting forward problems for camber to inverse problems for thickness, and forward problems for thickness to inverse problems for camber. A real tongue-twister, but the results were correct and elegant. Unfortunately, the methods applied to constant density irrotational flows only, so that extensions for nonlinear compressibility were impossible. In my second ASME paper on transonic flows with shocks, I found ways to circumvent Cauchy-Riemann conditions and complex variables, but the inverse formulations were restricted to planar problems. Still I labored. In the third ASME paper, I would extend the prior models to three dimensions. At first, this was wishful thinking. While f_xx + f_yy = 0 easily generalizes to f_xx + f_yy + f_zz = 0, everyone knows that y_xx + y_yy = 0 does not transform to y_xx + y_yy + y_zz = 0 because streamfunctions become vectors in three dimensions.

However, an alternative formalism was developed, making "scalar streamfunction-like" y’s satisfying y_xx + y_yy + y_zz = 0 legitimate. Still, dissatisfaction reigned supreme. I had assumed velocities derivable from potentials, but I sought methods allowing strong background shear flows. My fourth ASME paper solved the problem. Instead of "Ñ x q = 0, thus q = Ñf," I started with the less restrictive vorticity law y_xx + y_yy = U"(y)/U(y) y allowing use of "potential-like functions" that actually satisfied f_xx + f_yy = 0 with minor changes. I was able to develop models for general horizontal velocities U(y), but I was restricted to constant density flows. Meaning no transonics and no shockwaves. The year was 1984, forty years ago. At that point, I had almost completed what I had set out to do, however a unified theory integrating forward and inverse models for transonic flows, with strong shears and three-dimensionality was still lacking. But I would "forget" the problem and focus my efforts entirely in the petroleum geosciences.

Fast forward four decades. Time flies. In the intervening time, I would survive two life-threatening events, the first being undiagnosed appendicitis, followed by Deep Vein Thrombosis. That is, DVT or blood clots in both legs in the midst of Covid-19 and untested vaccines. That was the bad news. But in every cloud, there is a silver lining. Or two. I tired of ultrasound and endless injections while strapped to my hospital bed. I had worked on oil field "formation testers," ten-thousand pound, ten-feet long monster instruments that literally sucked oil from rock, predicting permeability and compressibility from fluid pressure transients. My invention would find applications in medical imaging, having accidentally realized that syringes were no more than miniature formation testers. From my hospital suite, the "Intelligent iSyringe" was born, testament to Nature’s awesome power in randomly extracting good from bad.

We have developed attractive slides showing various aircraft, e.g., F-35, F-47, J-36, J-20, Rafale, MIG, GCAP and others, operating in different flight environments. That’s close ground proximity, strong horizontal shear, supercritical shocks, and varied degrees of trailing edge closure supporting flapless wing control – focusing on bottom line themes central to reviving a declining interest in theoretical aerodynamics and stimulating CFD developments beyond "exact" but restrictive potential flows. These motivating visuals explain how special algorithms support modeling objectives. They may not be essential to experienced researchers, but our presentations are important to novices and practicing engineers. At the same time, we will not fall prey to "semantic traps" that preclude idea developments that really count. This is important to the author, who aspires to educate new generations of students who would otherwise would fall prey to thought-limiting vision. We will not start and stop at "Ñ x q = 0, thus q = Ñf," or "Ñ · q = 0, thus q = Ñ x y," limiting readers to restrictive models, but introduce flexible, rigorous "potential-like" and "streamfunction-like" extensions, along with almost three dozen practical "mini-thesis" examples demonstrating their unique strengths. Furthermore, all software will be offered to industry and the general public. And that means everybody.

Present Euler and Navier-Stokes solvers, while offering flexibility, are difficult to use and involve non-standard techniques that vary among developers. Software models remain isolated and narrow domains of research at independent labs. Potential flow, Euler and Navier-Stokes approaches do not offer sequential improvements to physical description. Results can be erratic and comparisons difficult. These comments are not stated capriciously. They result from years of interaction with developers, aerospace organizations and university groups. The work in this book introduces new approaches to old problems. Not "hand waving" methods, but rigorous ones developed to high scientific standards. Why require Ñ x q = 0 and f_xx + f_yy = 0 when less restrictive vorticity conditions based on y_xx + y_yy = U"(y)/U(y) y lead to a much more powerful f_xx + f_yy – 2U’(y)/U(y) f_y + f_zz = 0 that is very encompassing? Here U(y) is the background shear flow velocity. Why solve inverse problems using f_xx + f_yy = 0 with prescribed tangential derivatives f_x = - ½ C_p when y_xx + y_yy = 0, y_y = - ½ C_p plus Kutta-type constraints on trailing edge closure provide immediate, accurate solutions? These simple approaches are extended to full transonic nonlinearity with shear. And to all believing that scalar streamfunctions are not possible three-dimensionally, thanks to "Ñ · q = 0, thus q = Ñ x y," we show that y_xx + y_yy + y_zz = 0 and its extensions to include compressibility and shear do arise from atypical but rigorously correct statements on mass conservation. These ideas are developed and detailed suites of demanding validations are offered in theoretical discussions with examples to 6th Generation fighters such as F-35, F-47, J-36, J-20, Rafale, MIG, GCAP and others, operating in diverse flight environments – low ground proximity, strong horizontal shear, supercritical shocks, and different degrees of trailing edge closure supporting flapless wing navigation. Alone or simultaneously. New math and physics-based models were motivated with Deepseek-R1, AI/ML LLM interaction, and competing Large Language Models are also evaluated with respect to transonic aerodynamics. All "thinking" transcripts are provided for reference, while all algorithms and simulation-driven code developed by the author will be offered for industry use. In the meantime, Windows software executables (with red highlighted names) used to create our published examples will be available to readers at nominal cost with the aim of enhancing collaborative efforts. And finally, it’s great to be back – and thanks for your interest.