Year: 2024
Type: article
Abstract: For problems with very fine surface meshes, typically the most time-consuming step of a boundary element method (BEM, also called a panel method) is solving the final linear system of equations. Many have already studied how to efficiently solve the dense, asymmetric systems which arise in elliptic BEMs. However, this has not been studied for a supersonic aerodynamic BEM, for which the governing PDE is hyperbolic. Due to this hyperbolic character, the matrix equation which arises from a supersonic BEM has a large number of identically zero elements. But the resulting linear system of equations is also not sparse in the standard sense. Hence, the efficient solution of the linear system of equations arising in a supersonic BEM is here considered. A novel sorting algorithm is developed whereby the non-zero elements may be arranged into a useful structure with minimal cost. A novel direct solution method is developed here based on fast Givens rotations and the QR decomposition. This novel solver leverages the unique matrix structure to solve the supersonic system of equations more quickly than traditional direct methods. This novel method is then compared to other direct and iterative matrix solvers and is shown to be more robust than iterative solvers and more efficient than other direct solvers, with a computational time complexity of approximately O(N2.5).
Source: Aerospace
Authors: Cory Goates, Douglas Hunsaker
Institution: Utah State University
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,728
Awards: TO ENABLE COMMERCIALLY VIABLE CIVIL SUPERSONIC TRANSPORT (SST) AIRCRAFT INNOVATIVE SOLUTIONS MUST BE DEVELOPED TO MEET NOISE AND EFFICIENCY REQUIREMENTS FOR OVERLAND FLIGHT. THIS EFFORT EMPLOYS A MULTIDISCIPLINARY TEAM OF ACADEMIC AND INDUSTRIAL EXPERTS TO EXPLORE FOR THE FIRST TIME THE POTENTIAL OF SMALL REAL-TIME GEOMETRIC OUTER MOLD LINE (OML) RECONFIGURATIONS TO MINIMIZE BOOM SIGNATURES AND DRAG IN RESPONSE TO CHANGING AMBIENT CONDITIONS. THIS WILL ENABLE NOISE-COMPLIANT SST FLIGHT FROM TAKEOFF TO LANDING. OUR TEAM EXPLOITS ADVANCES IN LOW-VOLUME ENERGY-DENSE SOLID-STATE SHAPE MEMORY ALLOY (SMA) ACTUATORS THE MODELING THEREOF PROVEN SUPERSONIC COMPUTATIONAL FLUID DYNAMIC METHODS AND SONIC BOOM PROPAGATION TOOLS TO CONSIDER EMBEDDED SOLUTIONS FOR IN SITU ADJUSTMENT OF AN SST AIRCRAFT FOR AN OPTIMAL LOW BOOM SIGNATURE AND LOW DRAG IN DIFFERENT ENVIRONMENTS. PREVIOUS RESEARCH EFFORTS HAVE SHOWN THAT SMALL DISTRIBUTED CHANGES IN SST OML CAN SUBSTANTIALLY REDUCE PERCEIVED SONIC BOOM NOISE WITHOUT NEGATIVELY AFFECTING AERODYNAMIC PERFORMANCE. HOWEVER SIGNATURES OPTIMIZED THROUGH OML SHAPING AT A SINGLE FLIGHT CONDITION DEGRADE RAPIDLY WITH SLIGHT CHANGES IN FLIGHT CONDITION. ANGLE OF ATTACK ALTITUDE AIR DENSITY AND SPEED ARE KNOWN TO SIGNIFICANTLY IMPACT BOOM SIGNATURE AND SST FLIGHT PERFORMANCE ENDANGERING TRUE COMMERCIAL VIABILITY OF OVERLAND SUPERSONIC FLIGHT. TO BE COMMERCIALLY VIABLE A SST MUST ROBUSTLY MEET BOOM SIGNATURE LIMITS FOR A RANGE OF FLIGHT CONDITIONS AND THUS REQUIRES REAL-TIME ADAPTABILITY. THE NOVEL MULTIDISCIPLINARY AND STRUCTURALLY INTEGRATED EFFORT EXPLORES NEW ENGINEERING TOOLS AND MATERIALS DEMONSTRATING THAT DISTRIBUTED STRUCTURAL ADAPTIVITY CAN ENABLE ROBUST LOW BOOM SST PERFORMANCE IN VARYING CONDITIONS AND THUS DEVELOPS TECHNOLOGIES TO ENABLE COMMUNITY-ACCEPTED SST AIRCRAFT. OUR TEAM WAS CAREFULLY CHOSEN TO ADDRESS THIS UNIQUE AERONAUTICS PROBLEM IS STRONG IN EACH IMPORTANT TECHNICAL AREA AND IS SYNERGISTIC ACROSS MULTIPLE DISCIPLINES AND IDENTIFIED CHALLENGES. THE TEXAS A&M LEADERSHIP IS NATURAL FOR THIS EFFORT GIVEN ITS MANY PREVIOUS INTERDISCIPLINARY RESEARCH SUCCESSES AND LONG HISTORY OF SMART MATERIALS AND STRUCTURES DEVELOPMENTS AND SUPERSONICS/HYPERSONICS EXPLORATION. PARTNER INSTITUTIONS (FLORIDA INTERNATIONAL UNIVERSITY PRINCETON UNIVERSITY OF HOUSTON UNIVERSITY OF NORTH TEXAS UTAH STATE) WERE CHOSEN ON THE BASIS OF THEIR TECHNICAL CAPABILITIES AND PROVIDE NEW OPPORTUNITIES FOR SUPPORTING NASA S MISSION OF EXTENDING INCLUSION TO A WIDER RANGE OF RESEARCHERS. INDUSTRIAL PARTNERS (ATA ENGINEERING BOEING FORT WAYNE METALS) WERE SELECTED FOR THEIR BACKGROUND IN SUPERSONIC PLATFORM AND APPLICATION DEVELOPMENT AND UNDERSTANDING OF SHAPE MEMORY ALLOYS. THE OVERALL RESEARCH STRATEGY IS COMPOSED OF THREE MAJOR FOCUS AREAS OR TECHNICAL CHALLENGES THAT MUST BE MET FOR PROGRAM SUCCESS: I) DISTRIBUTED ADAPTIVITY DESIGN TOOLS DEVELOPMENT AND TRADE STUDIES II) MATERIALS DEVELOPMENT AND INTEGRATED SOLID-STATE ACTUATION DESIGN; AND III) DETAILED DESIGN AND DEMONSTRATION. INITIALLY THE TEAM IS IDENTIFYING POTENTIAL APPLICATIONS WHERE SMALLSCALE DISTRIBUTED ADAPTIVITY CAN PROVIDE A BENEFIT IN NOISE OR DRAG ACROSS THE ENTIRE FLIGHT ENVELOPE. FOR SELECTED APPLICATIONS/STRUCTURAL LOCATIONS REQUIRED OML GEOMETRY CHANGES WILL BE DETERMINED BASED ON ANALYSIS OF BOOM GROUND SIGNATURE AND DRAG REDUCTION USING NEW DESIGN TOOLS AND TRADE STUDIES. ADAPTIVE STRUCTURE DESIGNS WILL BE DEVELOPED AND EVALUATED AGAINST THE REQUIREMENTS (E.G. LOADING STROKE LENGTH OPERATIONAL TEMPERATURE) INCLUDING THE DEVELOPMENT OF NOVEL ALLOY FORMULATIONS TAILORED FOR BOTH AUTONOMOUS AND CONTROLLED ACTUATION. AS THE SMA MATERIAL DEVELOPMENT MATURES INTEGRATED SYSTEM-LEVEL FACTORS WILL BE CONSIDERED. OPTIMIZED DESIGNS FOR SELECTED ADAPTIVE STRUCTURAL APPLICATIONS WILL THEN BE MATURED AND TESTED MOVING TOWARD SYSTEM-LEVEL WIND TUNNEL DEMONSTRATION OF THE INNOVATIVE TECHNOLOGY APPROACHES AT A TRL 4-5., G1213555449, G2651657691, G58234515
OpenAlex ID: W4405281791